Question

Find the value of ${}^{\prime }{a}^{\prime }$ for which the vector $\overline{A}=3\hat{i}+3\hat{j}+9\hat{k}$ and $\overline{B}=\hat{i}+a\hat{j}+3\hat{k}$ are parallel.

Answer 1

Given $\overrightarrow{A}=3\hat{i}+3\hat{j}+9\hat{k}$ and $\overrightarrow{B}=\hat{i}+a\hat{j}+3\hat{k}$

Given , Vectors are parallel so $\overrightarrow{A}\times \overrightarrow{B}=0$

$(3\hat{i}+3\hat{j}+9\hat{k})\times (\hat{i}+a\hat{j}+9\hat{k})=(9-9a)\hat{i}+(9-9)\hat{j}+(3a-3)\hat{k}=0$

$\Rightarrow a=1$