Question
For what value of $\lambda$ are the vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ perpendicular to each other if
$\vec{\text{a}}=2\hat{\text{i}}+3\hat{\text{j}}+4\hat{\text{k}}$ and $\vec{\text{b}}=3\hat{\text{i}}+2\hat{\text{j}}+\lambda\hat{\text{k}}$

Answer

If the vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ are perpendicular to each other, then$\vec{\text{a}}.\vec{\text{b}}=0$
$\Rightarrow\Big(2\hat{\text{i}}+3 \hat{\text{j}}+4\hat{\text{k}}\Big).\Big(3\hat{\text{i}}+2\hat{\text{j}}-\lambda\hat{\text{k}}\Big)=0$
$\Rightarrow6+6-4\lambda=0$
$\Rightarrow12-4\lambda=0$
$\Rightarrow4\lambda=12$
$\Rightarrow\lambda=3$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free