Question

The resultant of vector P and Q is maximum when the angle between them is?

Answer 1

The resultant of vectors P and Q has maximum magnitude when the angle between them is 0°.

We have the expression for the magnitude of the resultant of P and Q,

√(P² + Q² + 2PQcosθ)

where θ is the angle between P and Q.

Here the magnitude of the resultant is also controlled by the cosine of the angle, θ.

To get maximum value for the resultant, cosθ should be maximum. And we know that the maximum value of cosθ is 1.

Well, cosθ = 1 implies θ = 0°.

In this case the magnitude of the resultant is P + Q, which is the maximum value.