Question

Two forces makes an angle 2α and their resultant makes an angle theta with the bisector of the angle between them show that p tan theta is equal to q tan alpha

Answer 1

Hi..

Case 1: alpha is zero

When alpha is zero, P makes an angle alpha (zero) with P. And if Q also makes an angle alpha (zero) with P, then the resultant would be P+Q (like scalar addition since P and Q are oriented in the same direction)

Case 2: P is zero

What if P is of zero magnitude? In that case, the direction of force (vector) P is indeterminate. So angle made by P with itself can be any angle, and hence it can also be alpha. Hence, the resultant would be Q (since P is zero and zero is the additive identity)

Hope this helps u!!