Question

Q8. If a and b are two vectors perpendicular to each other prove that
(a + b)^2 = (a - b)^2.
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Answer 1

Step-by-step explanation:

Q8. If a and b are two vectors perpendicular to each other prove that

(a + b)^2 = (a - b)^2.

Answer 2

Given:-

• a and b. such that a ⊥ b.

To Prove:-

• (a + b)² = (a - b)²

Proof:-

→ (a + b)²=  a·a + 2a·b + b·b = a² + 0 + b² = a² + b² -----(1)

(since a ⊥ b, a·b =0, and a·a=a², b·b =b² since angle between two parallel vectors is 0)

Similarly,

→ (a - b)² = a·a - 2a·b + b·b = a² - 0 + b² = a² + b² ------(2)

From (1) and (2), we get the desired result

→ (a+b)²= (a-b)²

HENCE PROVED!!