Question

Vector Q is 0.321 m long in a
123° direction. Vector S is
0.876 m long in a -32.1°
direction.
magnitude (m)
Find the magnitude of their vector sum

Answer 1

The magnitude of the vector sum of Q and S is determined as 0.6 m.

Resultant vector of Q and S

The magnitude of the vector sum of Q and S is determined from their resultant vector.

Qx = Qcosθ

Qy = Qsinθ

Qx = 0.321 x cos(123) = -0.175 m

Qy = 0.321 x sin(123) = 0.269 m

Sx = 0.876 x cos(-32.1) = 0.742 m

Sy = 0.876 x sin(-32.1) = -0.466 m

Qx + Sx = -0.175 m  + 0.742 m = 0.567 m

Qy + Sy = 0.269 m - 0.466 m = -0.197 m

Resultant vector

R = √[(0.567)² + (-0.197) ²]

R = 0.6 m

Thus, the magnitude of the vector sum of Q and S is determined as 0.6 m.

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