If the vectors `x hati-3hatj+7hatk and hati+yhatj-zhatk` are collinear then the value of `(xy^(2))/(z)` is equal

Options

A. `(9)/(7)`
B. `(-9)/(7)`
C. `(-7)/(9)`
D. `(7)/(9)`

Answer

B

Explanation

Given, vectors `xhati-3hatj+7hatk and hati+yhatj-zhatk` are collinear
`therefore(x)/(1)=(-3)/(y)=(7)/(-z)=k`
`impliesx=k,-3=ky and 7=-kz`
Now, `(xy^(2))/(z)=(k(-3)/(k))^(2))/(((-7)/(k)))=((9)/(k))/((-7)/(k))=(-9)/(7)`