You are given three vectors: A has a magnitude of 8.4 and is at an angle of 42 d

Question

You are given three vectors: A has a magnitude of 8.4 and is at an angle of 42 degree counterclockwise from the positive x-axis. B has a magnitude of 10.2 and makes an angle 24 degree counterclockwise of the positive y-axis. Chas a magnitude of 6.8 and makes an angle of 28 degree clockwise from the positive x-axis. Get the z and y components of A, B, and C Write the three vectors with unit vector notation. Calculate the following using unit vector notation: (A+ B), (A- C), (3A +2 C) and (-AB -3C+ A).

Explanation / Answer

here,

a)

Ax = 8.4 * cos(42) = 6.24 units

Ay = 8.4 * sin(42) = 5.62 units

Bx = - 10.2 * sin(24) = - 4.15 units

By = 10.2 * cos(24) = 9.32 units

Bx = 6.8 * cos(28) = 6 units

By = 6.8 * sin(28) = 3.19 units

b)

A = ( 6.24 i + 5.62 j ) units

B = ( - 4.15 i + 9.32 j ) units

C = ( 6 i + 3.19 j) units

c)

A + B = ( - 2.09 i + 14.94 j ) units

(A - C) = ( 0.24 i + 2.43 j) units

(3A + 2C) = ( 30.72 i + 23.24 j) units

( - 4B - 3C + A) = ( 4.84 i - 40.61 j ) units

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