Question

What can be the angle between (p+q)vector and (p-q)vector
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Answer 1

Answer:

angle between (P+Q) and (P-Q) may be acute, ... obtuse or 90%.

Answer 2

Answer:

cos θ=(p+q)×(p–q)/|p+q||p–q|.

So we need more information to deduce a specific angle.

It might be more clear to consider a parallelogram with adjacent sides P and Q. The P+Q and P-Q are its diagonals. Unless you know the lengths of the sides, we cannot proceed. Note that if P and Q have equal magnitudes, the parallelogram is a rhombus, in which case the angle between the diagonals is 90.

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