If the vectors 3 i + j + k and 2 i - j +8 k are perpendicular, th… - Vidyadip

Question

If the vectors $3\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}}$ and $2\hat{\text{i}}-\hat{\text{j}}+8\hat{\text{k}}$ are perpendicular, then $\lambda$ is equal to:

$-14$
$7$
$14$
$\frac{1}{7}$

✓

Answer

$14$

Solution:
It is given that vectors $3\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}}$ and $2\hat{\text{i}}-\hat{\text{j}}+8\hat{\text{k}}$ are perpendicular.
So, their dot product is zero.
$\big(3\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}}\big).\big(2\hat{\text{i}}-\hat{\text{j}}+8\hat{\text{k}}\big)=0$
$\Rightarrow6-\lambda+8=0$
$\Rightarrow14-\lambda=0$
$\therefore\lambda=14$

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