Question

1. What is angle between (A + B) and (A x B) ? both are vectors ​

Answer 1

Answer:

Explanation:

A and B are two vectors. So, their sum A +B lies in the same plane where A and B lies(assuming non -parallel etc so they define a plane and the cross product between them is not zero.)

A x B =| A ||B| sinα n, where α is the angle between A & B and n is the unit vector perpendicular to the plane containing A & B . So, the angle between (A+B) and (A x B) is 90° .

Mathematically,

|A +B||AxB|cosα=(A+B).(AxB)

= A.(AxB)+B.(AxB)

= B.(AxA)+A.(BxB)

= 0+0

=0

Therefore , cosα =0

α=90°