t Vector Math Practice Let vectors A (2,-1, 1), B (3,0,5), and C 1,4, 2), where

Question

t Vector Math Practice Let vectors A (2,-1, 1), B (3,0,5), and C 1,4, 2), where (ar, y, z) are the components of the vectors along i, j, and k respectively. Calculate the following: Part A Express your answer as an ordered triplet of components (z,y, z) with commas to separate the components. Submit Hints My Answers Give Up Review Part Part B Express your answer as an ordered triplet AI, BI, ICT with commas to separate the magnitudes. A, B, C Submit Hints My Answers Give Up Review Part Part C A. B Submit My Answers Give Up Part D Determine the angle between Band C Express your answer numerically in radians, to two significant figures. adians

Explanation / Answer

Here ,

A = (2 , -1 , 1)

B = (3, 0, 5)

C = (1, 4, -2)

Now,

2A + 3 B + C = (2 *2 + 3 * 3 + 1 , -1 *2 +3 * 0 + 4 , 1 * 2 + 5 * 3 - 2 )

2A + 3 B + C = (14 , 2 , 15)

the vector is (14 , 2 , 15)

B)

|A| = sqrt(2^2 + 1^2 + 1^2)

|A| = 2.45

|B| = sqrt(3^2 + 0 + 5^2)

|B| = 5.83

|C| = sqrt(1^2 + 4^2 + 2^2)

|C| = 4.58

the answer is (2.45 , 5.85 , 4.58)

C)

A.B = (2,- 1 , 1 ) . (3,0,5)

A.B = 2 * 3 - 1 * 0 + 1 * 5

A.B = 11

A.B is 11

D)

let the angle is theta between B and C

B.C = |B| |C| * cos(theta)

(3, 0,5).(1,4 ,-2) = 5.85 * 4.58 * cos(theta)

3 - 10 = 5.85 * 4.58 * cos(theta)

cos(theta) = -0.43

theta = 115.3 degree

the angle between B and C is 115.3 degree

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