Question
Write the value of p for which $\overrightarrow{a} = 3\hat{i} + 2\hat{j} + 9\hat{k}$ and  $\overrightarrow{b} = \hat{i} + \text{p}\hat{j} + 3\hat{k}$ are parallel vectors.

Answer

Since $\overrightarrow{a} || \overrightarrow{b}$  therefore $\overrightarrow{a} = \lambda \overrightarrow{b}$

$\Rightarrow (3\hat{i} + 2\hat{j} +9\hat{k} )=\lambda(\hat{i} + {p\hat{j} }+ 3\hat{k})$

$\Rightarrow \lambda = 3,\ 2 = \lambda p,\ 9 =3\lambda$

$\text{or} \lambda = 3, p = \frac{2}{3}$

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