AP EAMCET20225 Jul 2022Morning ShiftPhysicsMathematics in PhysicsActual
If two vectors A and B are mutually perpendicular, then the component of A - B along the direction of A + B is
Options
- A| A |^2+| B |^2
- B|A|^2-|B|^2
- C|A|^2-|B|^2 |A|^2+|B|^2
- D|A|^2+|B|^2 |A|^2-|B|^2
Correct answer
C. |A|^2-|B|^2 |A|^2+|B|^2
Step-by-step solution
The two vectors A and B are mutually perpendicular to each other A. B =0 A B =0 =0 =90^ | A - B | aligned & = A^2+B^2-2 A B 90^ & = A^2+B^2 aligned Unit vector along A - B = A - B | A - B | = A - B A^2+B^2 component of ( A + B ) in direction of ( A - B ) will be given as, = ( A + B ) ( A - B ) | A - B | = A A - A B + B A - B B A^2+B^2 = A^2-B^2 A^2+B^2 = | A |^2-| B |^2 | A |^2+| B |^2