Answers
Given:
The two vectors are:
[tex]\overrightarrow{a}=2\hat{i}-\hat{j}+\hat{k}[/tex]
[tex]\overrightarrow{b}=\hat{i}-3\hat{j}+5\hat{k}[/tex]
To find:
The value of [tex]|\overrightarrow{a}\times \overrightarrow{b}|[/tex].
Solution:
We have,
[tex]\overrightarrow{a}=2\hat{i}-\hat{j}+\hat{k}[/tex]
[tex]\overrightarrow{b}=\hat{i}-3\hat{j}+5\hat{k}[/tex]
The cross product of these two vectors is:
[tex]\overrightarrow{a}\times \overrightarrow{b}=\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\\2&-1&1\\1&-3&5\end{vmatrix}[/tex]
[tex]\overrightarrow{a}\times \overrightarrow{b}=\hat{i}[(-1)(5)-(1)(-3)]-\hat{j}[(2)(5)-(1)(1)]+\hat{k}[(2)(-3)-(-1)(1)][/tex]
[tex]\overrightarrow{a}\times \overrightarrow{b}=\hat{i}[-5+3]-\hat{j}[10-1]+\hat{k}[-6+1][/tex]
[tex]\overrightarrow{a}\times \overrightarrow{b}=-2\hat{i}-9\hat{j}-5\hat{k}[/tex]
Now the magnitude of the cross product is:
[tex]|\overrightarrow{a}\times \overrightarrow{b}|=\sqrt{(-2)^2+(-9)^2+(-5)^2}[/tex]
[tex]|\overrightarrow{a}\times \overrightarrow{b}|=\sqrt{4+81+25}[/tex]
[tex]|\overrightarrow{a}\times \overrightarrow{b}|=\sqrt{110}[/tex]
Therefore, the value of [tex]|\overrightarrow{a}\times \overrightarrow{b}|[/tex] is [tex]\sqrt{110}[/tex].
Related Questions
Help me please this awkward
Answers
Answer:
m<MLN =118°
Step-by-step explanation:
Because m<HIL and m<KLI are corresponding angles (equal)
and m<MLN am m<KLI are vertically opposite angles (equal)
find the area of the shape below
Answers
Answer:
235 cm²
Step-by-step explanation:
Find area of the large rectangle on the bottom. To do that, find its length and width, then multiply them together.
Length of big rectangle=20 cm
Width of big rectangle=9 cm
20x9=180 cm²
Next, find the area of the small rectangle on the top. To do that, find its length and width, then multiply them together.
Length of small rectangle=11 cm
Width of small rectangle=5 cm
I found the width by subtracting 9 from 14, since the 9 cm is part of the large rectangle.
11x5=55 cm²
Add the areas of the two rectangles.
55+180=235 cm²
Jasper's Pizzeria made 10 pizzas. 2 of the pizzas had pepperoni. What is the ratio of the number of pizzas without pepperoni to the number of pizzas with pepperoni?
Answers
Answer:
The ratio of pizzas with to without pepperoni is 8:2
Step-by-step explanation:
I hope this helps more than that person with the link!
the solution of a quadratic equation are 5 and -1. What is the factored form of a related quadratic fraction
A.f(x)=(x+5)(x-1)
B.f(x)=(x-5)(x+1)
C.f(x)(x-5)(x-1)
D.(x)=(x+5)(x+1)
Answers
[tex]\huge{\textbf{\textsf{{\color{pink}{An}}{\red{sw}}{\orange{er}} {\color{yellow}{:}}}}}[/tex]
A. f(x)=(x+5)(x-1)
For a rectangle with length of
3x + 4 and perimeter of 10x + 18,
what is the width of the
rectangle? Reminder, there are
two lengths and two widths in a
rectangle
Answers
Answer:
2x+5
Step-by-step explanation:
Formula for the perimeter of a reactangle= 2(l+b)
So,
2(l+b) = 10x+18
2(3x+4 + b) = 10x+18
Rearrange and solve
3x+4+b = 5x+9
b = 5x+9 - 3x - 4
b = 2x+5
Thus the measurement of the width = 2x+5
Hope this helps
Can you help me . Answer truthfully please I would really appreciate it.
Answers
Answer:
D must be the answer
Step-by-step explanation:
The area of the figure below is cm2. Round to the nearest
hundredth where necessary.
30 cm
30 cm
26 cm
Answers
Answer:
sorry the question is not clear enough
Haley substituted the values of a, b, and c into the quadratic formula below.
x = StartFraction negative (negative 10) plus or minus StartRoot (negative 10) squared minus 4 (7)(negative 2) EndRoot Over 2(7) EndFraction
What was Haley’s function in standard form?
f(x)=___x2+____x+____
Answers
Answer:
f(x) =
7
x2 +
-10
x +
-2
Step-by-step explanation:
Kathy dropped a snowball from a building that is 39.2 meters tall. The equation t2 = 39.29.8 represents the amount of time, in seconds, it takes for the snowball to reach the ground. How long did it take the snowball to reach the ground?
Answers
Answer:
We note that the equation that is compatible with the given equation is the kinematic equation of free fall where;
t² = 39.2 × 2/9.81
From which we have;
The time it takes the snowball to reach the ground is approximately 2.83 seconds
Step-by-step explanation:
The height of the building from which the ball is dropped, h = 39.2 m
The equation of the dropped a snowball, is given as follows;
t² = 39.2 × 9.8
Using the From the equation of free fall, we have;
s = u·t + 1/2·g·t²
Where;
u = The initial velocity = 0 m/s
t = The time of flight
g = The acceleration due to gravity = 9.81 m/s²
Therefore, we get;
∴ s = The height from which the snowball is dropped = 39.2 m
Therefore, we get;
39.2 = 0×t + 1/2×9.81×t²
∴ t² = 39.2 × 2/9.81 ≈ 7.99
t = √(7.99) ≈ 2.83
The time it takes the snowball to reach the ground, t ≈ 2.83 s.
Answer:
2 seconds
Explanation:
I had to do this assignment that's the correct answer
What is the area?Please i need help
Answers
Answer:
65
Step-by-step explanation:
Base by High
then divided by 2
HELP?! this is due today.
Answers
Answer:second choice
Step-by-step explanation:they would match up
What is the volume of the following rectangular prism?
Answers
Answer:
Step-by-step explanation:
It's going to be a mixed number.
Givens
L = 4 units
w*h = 2 1/8 units^2
V=L* (w*h)
V = 4 * (2 1/8)
V = 8 1/2
Where did the 1/2 come from?
You could write 2 1/8 as 2 + 1/8 and use the distributive property.
4(2 + 1/8)
4*2 + 4 * 1/8
8 + 4/8
4/8 = 1/2
8 1/2
b) The graph of y = x^2 + 1 is drawn on
the axes on the left.
Use the graph to estimate the
values of x when y = 4.
Give your answers to 1 decimal
place.
Answers
Answer:
(-1.7,1.7)
Step-by-step explanation:
OK, first draw the line y=4.
It's a bit misleading- where you think 4 should go is actually 2!
Check the scale and draw down where the two points meet on the line. They should be the same.
You get -1.7 and 1.7
The value of x is [tex]x=\pm\sqrt{3}[/tex]
Graph of parabola:The given function is;
[tex]y=x^{2} +1[/tex]
We have to find value of x when [tex]y=4[/tex]
[tex]y=x^{2} +1\\\\4=x^{2} +1\\\\x^{2} =4-1=3\\\\x=\pm\sqrt{3}[/tex]
Graph is also attached below.
Learn more about the parabola here:
https://brainly.com/question/12896871
what is the answer to 4x+7=-2+4x
Answers
0=(-9)
Step-by-step explanation:
4x + 7 = -2 + 4x
4x + 7 = 4x -2
subtract 7 from both sides of the equation.
simplify your answer.
subtract 4x from both sides of the equation.
simplify your answer again.
4x + 7 = 4x -2
___-7 = 4x -7
4x __ = 4x -9
__4x = 4x -9
-4x = -4x -9
__0 = -9
the input is a contradiction: it has no solutions.
Half of the sum of 3x and 4
Answers
Answer:
1/2(3x+4)
or
1/2(3x)+2
Step-by-step explanation:
Please help I willgive brainliest
Answers
Answer:
first one is Given:
line segment AD bisects line segment BE
angle B ≅ angle E
Prove:
△ABC ≅ △DEC
See attachment for picture.
I need to do this using the statement versus reasons chart.
the second one is is 42 i will provide a screenshot with the answer
Answer:
I think the answer is C, but I not sure
I hope this answer can help you
Step-by-step explanation:
180-126-16＝38
[tex] \frac{180 - 38 - 16}{3} = 42[/tex]
PLS HELP ASAP 10 POINTS
Erika has a collection of 300 movies. 2/5 of these movies were made after 2010. 50% of the movies were made between 1990 and 2010. The rest were made before 1990.
How many movies of Erika's collection were made before 1990?
Answers
Answer:
30
Step-by-step explanation:
300 * 0.4= 120
300*0.5 = 150
150+120=270
300-270=30
PLEASE HELP ASAP!
The table shows a linear function.
Which equation represents the function?
Answers
Answer:
The answer seems to be A
Step-by-step explanation:
Plz someone answer this for me asap !
Find the perimeter of each shape
Equation :
X:
Perimeter:
Answers
Answer:
The equation is;
4(2.5x-3) = 3(2x-2)
The value of x is 1.5
Step-by-step explanation:
Mathematically, the perimeter of a square is simply the product of the length of the side and 4
Secondly, the perimeter of an equilateral lateral triangle is the product of the length of its side and 3
Thus, mathematically, we have it that;
4(2.5x-3) = 3(2x-2)
10x - 12 = 6x -6
10x -6x = -6 + 12
4x = 6
x = 6/4
x = 1.5
can someone explain and tell me the answer plsss
Answers
Answer: it’s c
Step-by-step explanation: it’s c because you go five units down and then see how many units it is to reach the origin then go that amount of units up☺️I hope I could help!
Sarah is finding the surface area of a cube. Find the surface area of the cube with dimensions of 8 cm each
Answers
= 6x8x8
= 6x64
= 384 cm2
Hope this helps
Please mark brainliest
Answer:
384 cm^2
Step-by-step explanation:
A = 6a^2 (a = side length)
A = 6(8^2)
A = 6(64)
A = 384 cm^2
More explain stuff:
a^2 is what is used to find the area of a 2 dimensional square. You can also use a · a. Remember, a = side length. Since there are 6 sides/faces in a cube, you multiply the area of each face by 6. :D
According to the graphs below, which statement is true?
25
251
Number Preferred
Number Preferred
21
0
20
Brand A
Brand B
Brand A Brand B
Brand
Brand
2003 Gayriyon, no
The graph on the left is misleading
The graph on the right is misleading.
Both graphs show the information accurately.
Both graphs are misleading
Answers
Answer:
The graph on the right is misleading
Step-by-step explanation:
The brand preference is 21 to 25, which shows a slight advantage for Brand B. The graph on the right requires you to mindfully read the y axis to infer that - if you wouldn't, you'd think that Brand B dominates Brand A.
Answer:
The graph on the right is misleading.
Step-by-step explanation:
Solve the equation. 36^6x-1 = 6^5x
Answers
The solution of the equation 36⁶x - 1 = 6⁵x is x = 1/2176774560.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
We have the equation:
36⁶x - 1 = 6⁵x
Simplifying,
(6²)⁶x - 1 = 6⁵x
6¹²x - 6⁵x = 1
2176782336x - 7776x = 1
x = 1/2176774560
The above equation is the required solution.
Therefore, the required value is x = 1/2176774560.
To learn more about the equation;
https://brainly.com/question/12788590
#SPJ2
DISCLAIMER.......................................................................................................................................................................................................................................................................... 5000 x 800
K imma make another account (you'll know due to my first question). Anywho, If you are my friend or if i helped feel free to go to my new account and friend me!!! (Also anywho take 100 points and buff shrek
Answers
Answer: wut the ham is this
Q1 - What is the area of a circle with a diameter of 6.2 inches?
Q2 - A round table has a radius of 15in a round tablecloth hangs 2in over the edge of the entire table.what is the area of the tablecloth
Answers
Answer:
Q1; 124.72
Sorry I don’t understand the second one
Step-by-step explanation:
Omealio received a grade of 80 on Exam 1. If his grade in Exam 2 was 15% higher, what was his grade in Exam 2? Please help
Answers
Answer:
well if the max grade he could get was 100 then you need to find 15% of 100 which is 15, after that add 15 to 80 and you get 95.
his grade for exam 2 was 95
Step-by-step explanation:
15% of 100 = 15
80 + 15 = 95
Answer:
92
Step-by-step explanation:
15 percent of 80 is 12 percent
80 + 12 = 92
Someone help pls. hurry
Answers
Answer:
slope = -1/4 intercept = 50
Step-by-step explanation:
What is the product of 4 1/3 times 3 1/3?
12
12 2/3
12 7/9
14 4/9
Answers
Answer:
Hello! Your answer would be D) 14 4/9
Step-by-step explanation:
Hope I helped! Brainiest plz!♥
Have a nice morning! -Abby
Answer:
It is D
Step-by-step explanation:
Click on a factor pair of 12
Answers
Answer:
Step-by-step explanation:
x 12 = 12.
x 6 = 12.
x 4 = 12.
x 3 = 12.
PLEASE HELP!! NO LINKS PLEASE!!
Answers
Answer:
try looking for it in the settings
Step-by-step explanation:
can that helps