Question

.Assertion: When I P+ Q I = I P- QI, then P must be perpendicular to Q. Reason: The relation will hold even when Q is a null vector.

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Answer 1

Answer:

Let, β be the angle between vectors P and Q.

Now, vectors Q and -Q are having same magnitude; but they act in opposite directions.

So, angle between vectors P and -Q = (180° - β).

And, |-Q| = |Q|.

|P + Q|^2 = |P|^2 + |Q|^2 + 2 * |P| * |Q| * (cos β)

And,

|P - Q|^2 = |P|^2 + |Q|^2 + 2 * |P| * |Q| * cos (180° - β).

So, cos β = cos (180° - β) = - cos β

So, β = 90°.

Answer 2

Explanation:

this is the answer of this question

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