Question

Two forces, 3 N and 5 N respectively, act on the same point simultaneously. The magnitude of their resultant force is 2 N when the angle between them is _____.

Answer 1

The resultant of two vectors:

$\vec{P}$ and $\vec{Q}$ is given by

$R= \sqrt{ P^2+Q^2+2PQcosθ}$

where, P and Q are magnitudes of two vectors and θ is the angle between two vectors.

Here θ=? P=3 N Q=5 N R=2 N

Therefore,

$2 = \sqrt{3^2 + 5^2 +2 \times 3 \times 5 \times cosθ} \\ 4 = 9 + 25 + 30cosθ \\ 30cosθ = -30 \\ cosθ = -1 \\ θ = 180°$