First slide

Vectors

Question

The sum of the magnitudes of two forces acting at a point is 18 and the magnitude of their resultant is 12. If the resultant is at 90° with the force of smaller magnitude, what are the magnitudes of forces?

Moderate

A

12,6
B

14,4
C

5, 13
D

10,8

Solution

We have, P + Q = 18
and R= 12
$Qsinθ = P and Qcosθ = R$
Squaring and adding, we get
P² +R² = Q²
or Q² $-$ P² = R² = 144
Solving Eqs. (i) and (ii) , we get
P = 5 and Q = 13.

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