Vector A points in the negative x direction. Vector B points at an angle of 30° above the positive x axis. Vector C has a magnitude of 17 m and points in a direction 42.0° below the positive x axis. Given that A + B + C =0, find the magnitudes of A and B. 

Solution:

Given, vector A points in the negative x direction

Vector B points at an angle of 30° above the positive x axis.

Vector C has a magnitude of 17m and points in a direction of 42° below the positive x axis.

A + B + C = 0

We have to find the magnitude of A and B.

Vector A in the negative x direction is -a.

Vector B = bcos30° - bsin30°

Vector C = 17cos42° - 17sin42°

The system of equations are 

17 cos 42° + b cos 30° - a = 0 --- (1)

17 sin 42° - b sin 30° = 0 --- (2)

On solving (2),

17 sin 42° = b sin 30°

17(0.6691) = b (0.5)

11.3747 = 0.5b

b = 11.3747/0.5

b = 22.7494

|b| = 22.7494 m

Put the value of b in (1),

17(0.7431) + 22.7494(0.8660) - a = 0

12.6327 + 19.7009 = a

a = 32.33368

|a| = 32.3337 m

Therefore, the magnitudes of A and B are 32.3337m and 22.7494m.

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Vector A points in the negative x direction. Vector B points at an angle of 30.0° above the positive x axis. Vector C has a magnitude of 17 m and points in a direction 42.0° below the positive x axis. Given that A + B + C = 0, find the magnitudes of A and B. 

Summary:

Vector A points in the negative x direction. Vector B points at an angle of 30.0 ∘ above the positive x axis. Vector C has a magnitude of 17 m and points in a direction 42.0 ∘ below the positive x axis. Given that A + B + C = 0, the magnitudes of A and B are 32.3337m and 22.7494m.