Question

The resultant of A
and B
is perpendicular to B
What is the angle between A
and B
?

Answer 1

Answer:

Taking A and B as P and Q

Let θ be the angle between P and Q.

Let the resultant R make an angle α with P.

Given that α = 90°.

We have the formula

tan α = Q sin θ/(P + Q cos θ) sin α / cos α

= Q sin θ/(P + Q cos θ)

Cross multiplying , we get

(P+Q cosθ)sinα = Qsinθcosα(P+Qcosθ)sin 90°

= Q sin θ cos 90° (P + Q cos θ) = 0

⇒ cos θ = −P/Q θ = cos−1 (−P/Q)

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