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Scalar Or Dot Product — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsScalar Or Dot Product2 Marks
Question
Find the value of $\lambda$ is the vectors $2\hat{\text{i}}+\lambda\hat{\text{j}}+3\hat{\text{k}}$ and $3\hat{\text{i}}+2\hat{\text{j}}-4\hat{\text{k}}$ are perpendicular to each other.
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Answer

Given: $2\hat{\text{i}}+\lambda\hat{\text{j}}+3\hat{\text{k}}$ and $3\hat{\text{i}}+2\hat{\text{j}}-4\hat{\text{k}}$ are perpendicular to each other.
So, their dot product is zero.
$\big(2\hat{\text{i}}+\lambda\hat{\text{j}}+3\hat{\text{k}}\big).(3\text{i}+2\text{j}-4\text{k})$
$\Rightarrow6+2\lambda-12=0$
$\Rightarrow2\lambda-6=0$
$\Rightarrow\lambda=3$

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