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Vector Algebra — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVector Algebra1 Mark
Question
The value of $\lambda$ for which two vectors $2 \hat{i}-\hat{j}+2 \hat{k}$ and $3 \hat{i}+\lambda \hat{j}+\hat{k}$ are perpendicular is
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Answer

Dot product of two mutually perpendicular vectors is zero.
$(2 \hat{i}-\hat{j}+2 \hat{k}) \cdot(3 \hat{i}+\lambda \hat{j}+\hat{k})=0$
$\Rightarrow 2 \times 3+(-1) \lambda+2 \times 1=0$
$\Rightarrow 6-\lambda+2=0$
$\Rightarrow \lambda=8$

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