Question

The condition for A+B to be perpendicular to A-B is that​

Answer 1

Answer:

For two vectors ( a + b) and ( a - b ) to be parallel their cross product need to vanish ie

( a + b ) × ( a - b ) = 0

=> a × a + b × a - a × b - b × b = 0

=> 0 + b × a + b × a + 0= 0 ( because a×a =0, and b× b = 0)

==> 2 b × a = 0; or b × a = 0.

Or this implies that vectors a and b are parallel to each other.

The only way (a + b) and ( a - b) are parallel to each other is when a and b are themselves parallel to each other.

Answer 2

Answer:

Two vectors A and B are perpendicular if and only if their scalar product is equal to zero

Explanation:

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