Question

two vectors A1 and A2 each of magnitude are inclined to each other such that their resultant is equal to √3Afind the resultant of vectorA1 1 and -A1
vector

Answer 1

Here i m not clear if you are asking about the resultant of - A1 and A1 cause it will be zero but if it is A1 and A2 then we need calculate the magnitude and directions in terms of A

Answer 2

The resultant of vector A1 and -A1 is 0.

The magnitude both the vectors A1 and A2 is equal to A .

|A1| = A , |A2| = A

resultant of A1 and A2 = √3 A

=> √3 A = √(A² + A² + 2A² cos x)

=> 3A² = 2A² + 2A² cos x

=> 1/2 = cos x

x = 60°

The angle between A1 and A2 is equal to 60° .

Now , we have to find the resultant of A1 and -A1. The angle between these vectors = 180°

resultant of A1 and -A1 = √(A²+A²+2A² cos 180° )

=> √(2A²-2A²)

=> 0

The resultant of A1 and -A1 will be zero as they are equal in magnitude but opposite in direction.