If |a+b| = |a-b| then (a,b) = Options: A . &nbsp π 6 B . &nbsp π 4 C . &nbsp π 3 D . &nbsp π 2

Answer: Option D : D | a + b | = | a − b | ⇒ | a + b | 2 = | a − b | 2 ⇒ ( a + b ) 2 = ( a − b ) 2 ⇒ a 2 + b 2 + 2 a . b = a 2 + b 2 − 2 a . b ⇒ 4 a . b = 0 ⇒ a . b = 0 ⇒ ( a , b ) = 90 ∘

If |a+b| = |a-b| then (a,b) =

Discussion Forum : Vector Algebra

Question -

If |a+b| = |a-b| then (a,b) =

Options:

A .

\frac{π}{6}

B .

\frac{π}{4}

C .

\frac{π}{3}

D .

\frac{π}{2}

Answer: Option D
:
D

| a + b | = | a - b | \Rightarrow | a + b |^{2} = | a - b |^{2} \Rightarrow (a + b)^{2} = (a - b)^{2} \Rightarrow a^{2} + b^{2} + 2 a . b = a^{2} + b^{2} - 2 a . b \Rightarrow 4 a . b = 0 \Rightarrow a . b = 0 \Rightarrow (a, b) = 90^{\circ}

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