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Question: Answered & Verified by Expert
If $|\vec{a}|=4,|\vec{b}|=5$, then the values of $k$ for which $\vec{a}+k \vec{b}$ is perpendicular to $\vec{a}-k \vec{b}$ are
MathematicsVector AlgebraMHT CETMHT CET 2021 (23 Sep Shift 1)
Options:
  • A $\pm \frac{5}{4}$
  • B $\pm \frac{2}{5}$
  • C $\pm \frac{16}{25}$
  • D $\pm \frac{4}{5}$
Solution:
2391 Upvotes Verified Answer
The correct answer is: $\pm \frac{4}{5}$
$\begin{aligned} & (\vec{a}+k \vec{b}) \cdot(\vec{a}-k \vec{b})=0 \\ & \therefore|a|^2-k^2|b|^2=0 \\ & \therefore(4)^2-k^2(5)^2=0 \Rightarrow k= \pm \frac{4}{5}\end{aligned}$

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