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Question: The vector \(\overset{\rightarrow}{P} = a\widehat{i} + a\widehat{j} + 3\widehat{k}\) and \(\overset{...

The vector P→=ai^+aj^+3k^\overset{\rightarrow}{P} = a\widehat{i} + a\widehat{j} + 3\widehat{k} and Q→=ai^−2j^−k^\overset{\rightarrow}{Q} = a\widehat{i} - 2\widehat{j} - \widehat{k} are perpendicular to each other. The positive value of a is

A

3

B

4

C

9

D

13

Answer

3

Explanation

Solution

Pˉ.Qˉ=0\bar{P}.\bar{Q} = 0∴ a2−2a−3=0a^{2} - 2a - 3 = 0⇒a=3a = 3