Mathematics | MHT CET 2019 | Discussion Page

The vectors $x\hat{i}-3\hat{j}+7\hat{k}$ and $\hat{i}+y\hat{j}-z\hat{k}$ are collinear then the value of

$\frac{xy^{2}}{z}$ is equal

$\frac{9}{7}$

$\frac{-9}{7}$

$\frac{-7}{9}$

$\frac{7}{9}$

Option B

Given, vectors $x\hat{i}-3\hat{j}+7\hat{k}$ and $\hat{i}+y\hat{j}-z\hat{k}$ are collinear

$\therefore$ $\frac{x}{1}=\frac{-3}{y}=\frac{7}{-z}=k$

$\Rightarrow$ x=k, -3=ky and 7=-kz

Now, $\frac{xy^{2}}{z}=\frac{k(-\frac{3}{k})^{2}}{(\frac{-7}{k})}=\frac{\frac{9}{k}}{\frac{-7}{k}}=\frac{-9}{7}$

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