First slide

Vectors

Question

The sum of two forces acting at a point is 16 N. If the resultant force is 8 N and its direction is perpendicular to minimum force then the forces are

Moderate

A

6 N and 10 N
B

8 N and 8 N
C

4 N and 12 N
D

2 N and 14 N

Solution

A+B = 16(given) ……..(i)
$tanα = \frac{Bsinθ}{A + Bcosθ} = \tan 90^{0}$
$∴$ A+ $Bcosθ = 0 \Rightarrow cosθ = \frac{- A}{B}$ ……(ii)
8 = $\sqrt{A^{2} + B^{2} + 2 ABcos θ}$ ……..(iii)
By solving eqs. (i), (ii) and (iii) we get
A = 6 N, B = 10 N

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