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The value of $λ$ for which two vectors $a = 5 \hat{i} + λ \hat{j} + \hat{k} and b = \hat{i} - 2 \hat{j} + \hat{k}$ are perpendicular to. each other is

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detailed solution

Correct option is C

For two vectors a and b to be perpendicular, a · b = 0Thus, (5i^+λj^+k^)·(i^-2j^+k^)=05(i^·i^)-2λ(j^·j^)+1(k^·k^)=0⇒ 5-2λ+1=0⇒ 6-2λ=0⇒λ=3

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The value of λ for which two vectors a=5i^+λj^+k^ and b=i^-2j^+k^ are perpendicular to. each other is

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The value of $λ$ for which two vectors $a = 5 \hat{i} + λ \hat{j} + \hat{k} and b = \hat{i} - 2 \hat{j} + \hat{k}$ are perpendicular to. each other is