Mathematics College

Consider the following vectors.
u = i + 4 j − 2 k, v = 4 i − j, w = 6 i + 7 j − 4 k
Find the scalar triple product u · (v ⨯ w).
u · (v ⨯ w) =
Are the given vectors coplanar?
Yes, they are coplanar.
No, they are not coplanar.
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Consider The Following Vectors.u = I + 4 J 2 K, V = 4 I J, W = 6 I + 7 J 4 KFind The Scalar Triple Product

Answers

Answer 1

The scalar triple product is 0.

If v = 4i - j and w = 6i + 7j - 4k, then their cross product is

v × w = (4i - j) × (6i + 7j - 4k)

v × w = 24 (i × i) + 28 (i × j) - 16 (i × k) - 6 (j × i) - 7 (j × j) + 4 (j × k)

v × w = 28k - 16 (-j) - 6 (-k) + 4i

v × w = 4i + 16j + 34k

and

u • (v × w) = (i + 4j - 2k) • (4i + 16j + 34k)

u • (v × w) = 4 + 64 - 68

u • (v × w) = 0

Yes, they are coplanar.

The vectors v and w together span a plane. v × w is a vector that is perpendicular to this plane. Since the dot product of u with this vector is 0, this means u is perpendicular to v × w, which in turn means that u is in the same plane as v and w.

Related Questions

Put x + 2y=4 into slope-intercept form? y=mx+b format

Answers

Answer:

[tex]y=-\frac{1}{2} x+2[/tex]

Step-by-step explanation:

1.  First we want to get the y all by itself

So we would subtract x from both sides and get [tex]2y=-x+4[/tex]

2. Then we would divide 2 from both sides

Answer: [tex]y=-\frac{1}{2} x+2[/tex]

the qustion is to make 5 dinner rolls 1/3 cup of flour is used how much flour is needed to make 1 dinner roll​

Answers

Answer:

[tex]\frac{1}{15}[/tex] cup of flour

Step-by-step explanation:

5 rolls = [tex]\frac{1}{3}[/tex] cup

? × 5 = [tex]\frac{1}{3}[/tex]

[tex]\frac{1}{3}[/tex] ÷ 5 = ?

[tex]\frac{1}{3}[/tex] ÷ [tex]\frac{5}{1}[/tex] = [tex]\frac{1}{3}[/tex] × [tex]\frac{1}{5}[/tex] = [tex]\frac{1}{15}[/tex]


If you need to find the value of a variable in an equation, you need to
equation, which means to find the set of values that makes the equation true.
A.isolate
B.simplify
C.check
D.solve

Answers

A isolate the variable

HELP!!!!!!!!!!!!!!!! I WILL GIVE BRAINILEST.

Answers

Answer:

B. 2/5

Step-by-step explanation:

dividing by 2 both numerator and denominator we get

2/5

hope it helps u

mark me brainliest pls

15. Tom is deciding whether or not he should become a gym member to use their basketball courts. The membership cost is $135. Members pay $3 to rent out the basketball courts. Non-members can rent the courts also, but they have to pay $11 each time. How many times would Tom need to rent the court in order for it to be cheaper to be a member than a non-member?​

Answers

Answer:

Tom need to rent the court in order for it to be cheaper more than 15 times.

Step-by-step explanation:

Answer:

Tom needs to rent it atleast 17 times.

Step-by-step explanation:

1) First, write your equations. x in this case equals the # of times you rent the court.

For members: y = 135 + 3x (members)

Non-members: y = 11x (non-members)

From here, there can me many methods that can work. Right now I can only think of one though :/.

So what you can do is plug in numbers and see what happens. I suggest you work with easy numbers when you plug stuff in. Once you find that non-members is greater than the amnt for members have, that's your answer!

a) x = 10

For members: 135 + 3(10) = 165

Non-members: 11(10) = 110

Didn't work. :(

b) x = 20

For members: 135 + 3(20) = 195

Non-members: 11(20) = 220

Aha! We have a valid answer. However, we need to find the minimum number of times Tom needs to rent it.

c) x = 15

For members: 135 + 3(15) = 180

Non-members: 11(15) = 165.

So our answer is between 15 and 20.

If you keep doing this, you'll find that 18 is the minimum number of times tom will have to rent the court. So your answer is anything greater than equal to 17.

x = 17

For members: 135 + 3(17) = 186

Non-members: 11(17) = 187

Sorry I made this tedious, but this is one method. Though I helped you find the answer, I hope someone else can help you find the best method!

select another name for m<1
please help.

Answers

Answer:

<DAC

Step-by-step explanation:

label angles with their variable points

4 is the _____ of 4n

Answers

Answer:

4 is the coefficient of 4n

Step-by-step explanation:

An employee earns $10.75 per hour. Write an equation that represents the total earnings in a week, y, as it relates to time in hours? Use your equation to find the total earnings for a 40 hour week.

Answers

Answer:

40 X 10.75= 430  

10.75/2= 5.375 round up 5.38  

10.75 + 5.38 = 16.13  

16.13 X 10 = 161.30  

430+161.30= 591.3

Which expression uses the associative property to make it easier to evaluate 14(1/7 2/5)?
A. 14(2/5.1/7)
B. 7(1/14.2/5)
C. (14.5/2)1/7
D. (14.1/7)2/5

Answers

Answer:

B

Step-by-step explanation:

Answer:

A. 14(2/5.1/7)

Step-by-step explanation:

A Tourist Information Center is between a Bus Station and a Train Station. When mapped on a grid, the Tourist Information Center is
located at (15,2) and the Bus Station is located at (5,-10).
The Train Station is located at point?

Answers

Answer:

A Tourist Information Center is between a Bus Station and a Train Station. When mapped on a grid, the Tourist Information Center is

located at (15,2) and the Bus Station is located at (5,-10).

The Train Station is located at point?

Write each fraction as a decimal and as a percent.​

Answers

Answer:

0.35 and 35%

Step-by-step explanation:

7/20=35/100

35/100=0.35=35%

Help me please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

2.02

Step-by-step explanation:

Hi, need help on this simple division question (:

Answers

Answer:

775

Step-by-step explanation:

186÷0.24=775

your welcome

I need help in statistics
​

Answers

Answer:

What help you neep? Please ask with out no fear

Hello need help on this question (:

Answers

Answer:

the answer is B. the 2 in the hundredths place is 1/10 the 2 in the tenths place

Simplify 3xy²-2a²b-4xy²+8a²b​

Answers

Answer: 6a^2b - xy^2

Step-by-step explanation:

Answer:

If you EVALUATE it is [tex]6ba^{2}[/tex] - [tex]xy^{2}[/tex]

Differentiate w.r.t. x means the answer is

[tex]-y^{2}[/tex]

Step-by-step explanation:

PLS HELP EN UNDERSTAND THIS

Answers

Answer:

-5.5x+5.8

Step-by-step explanation:

To do this you need to remove the parenthesis and subtract like terms only (-3.6x - 1.9x) and the same thing for the other like terms.

WILL GIVE BRAINILEST TO CORRECT ANSWER! TYSM IF U ANSWER :D


Compare each pair of fractions. Use <, =, or >.

2/3____5/8


Answers:

A. >
B. <
C. =

Answers

Answer:

>

2/3 is bigger than 5/8 because 5/8 is split into smaller portions

Step-by-step explanation:

hope this helps

Q9) When working on a problem recently, Mya saw the polynomial expression 4 - 3x”. She decided to
re - write it as - 3x + 4. Which property of real numbers justifies (allows) Mya's action? Explain your
answer.

Answers

Answer:

Commutative Property of Addition

a + b = b + a

which says

"commute = to get up and move to a new location : switch places"

4-3x = -3x +4



Luke owns a 1200 ft2 apartment. If
Luke is planning on tiling of his
apartment's total square footage and
Home Depot charges $6.75 for 1 ft of
tile. How much money will Luke
spend on tiling his apartment?

Answers

Answer:

$8100

Step-by-step explanation:

= 1200 *6.75=$8100

HELP ME ON THIS QUESTION PLZ!!!

Answers

x + 10 + x + 10 = 2x + 20

= 2 (x + 10)

So, option (d) is correct

Please answer this problem worth 59 pts

Answers

Answer:

35.2

Step-by-step explanation:

Find the missing angle:

m∠L = 180° - 60° - 45° = 75°

Use the law of sines to determine the lengths of the sides:

LM / sin ∠K = KM / sin 75°12 / sin 60° = KM / sin 75KM = 12 sin 75° /sin 60° = 13.4 (rounded)KL / sin ∠M = LM / sin ∠KKL / sin 45° = 12 / sin 60°KL = 12 sin 45° / sin 60° = 9.8 (rounded)

Find perimeter:

P = 12 + 13.4 + 9.8 = 35.2

Please help fast !!!!!!!!!

Answers

Answer:

x >= -2

Closed circle and going to the right, so it is greater than or equal to -2.

Help please thanksss

Answers

Yes because of AAA. They have the same angles, so their sides must also be proportionate, making them congruent

Find the solution of the system of equations. 6x -y= 21. -5x + y= -18​

Answers

First one is -6 and the second one is -3

Which expression shows the result of applying the distributive property to 3(1/5x−1/7)?


3/5x+3/7

−3/5x+3/7

−3/5x−3/7

3/5x−3/7

Answers

Answer:

d. 3/5x−3/7

Step-by-step explanation:

Use distributive property.

3(1/5x−1/7)(3×1/5x) - (3×1/7)3/5x - 3/7

∴ choice d. 3/5x−3/7 is correct.

A is the point (8, 5) and B is the point(- 4, 1).Calculate the length of AB. *

Answers

Answer:

..............................

How do you solve 14x14x14?

Answers

Answer:  2744

Step-by-step explanation: 14x14= 196 x14 =2744

Answer:

The answer is 2744.

Step-by-step explanation:

First solve for 14 x 14, which is 196.

Then solve for 196 x 14, which is 2744.

Hence, the answer is 2744.

PLEASE MARK AS BRAINLIEST!!!!!

anyone have the answer to this one?

Answers

Area of the rectangle is 60

Area of the semi circle 14.13 ir 14.1

60 plus 14.1 is 74.1

I hope its right

the area of it is 60!

Queens help me solve this
-0.125(0.25x - 0.5)

Answers

Answer:

−0.03125x + 0.0625

Step-by-step explanation:

Answer:

0.03125x−0.0625

Step-by-step explanation:

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