Discussion Forum

 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 

Answer:

Explanation:

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