± Vector Dot Product Learning Goal: To understand the rules for computing dot pr

Question

± Vector Dot Product Learning Goal: To understand the rules for computing dot products. Let vectors A=(2,1,4), B=(3,0,1), and C=(1,1,2).

Part A - Dot product of the vectors A and B

Calculate AB.

Express your answer numerically.

Part B - Angle between the vectors A and B

What is the angle AB between A and B?

Express your answer numerically to three significant figures in radians.

Part C - Dot product of two vectors multiplied by constants

Calculate 2B3C.

Express your answer numerically.

Part D - Multiplication of a dot product by a scalar

Calculate 2(B3C).

Express your answer numerically.

Part E - Dot product of a vector and a scalar?

Which of the following can be computed?

Which of the following can be computed?

Let V1 and V2 be different vectors with lengths V1 and V2, respectively.

Part F - Dot product of a vector with itself

Calculate V1V1.

Express your answer in terms of V1.

Part G - Dot product of two perpendicular vectors

If V1 and V2 are perpendicular, calculate V1V2.

Express your answer numerically.

Part H - Dot product of two parallel vectors

If V1 and V2 are parallel, calculate V1V2.

Express your answer in terms of V1 and V2.

Explanation / Answer

Here , for the vectors

A = (2, 1 , -4)

B= (-3, 0 , 1)

C = (-1 , -1 , 2)

part A)

A.B = 2 * (-3) + 1 * 0 - 4 * 1

A.B = -10

part B)

let the angle is theta

cos(theta) = -10/(sqrt(2^2 + 1^2 +4^2) * sqrt(3^2 + 0 + 1^2))

cos(theta) = - 0.69

theta = 133.6 degree

the angle between A and B is 133.6 degree

c)

for the 2B . 3C

2B . 3C = 6 * (3 * 1 + 0 + 1 * 2)

2B . 3C = 6 * 5

2B . 3C = 30

d)

for the 2(B.3C).

2(B.3C) = 6 * B.C

2(B.3C) = 30

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