Question

The vectors $xi-3j+7k$ and $i+yj-zk$ are collinear then the value of $\frac{x{y}^2}{z}=$

• A. $\frac{9}{7}$
• B. $-\frac{9}{7}$
• C. $\frac{6}{7}$
• D. $-\frac{6}{7}$

Answer 1

The correct option is B $-\frac{9}{7}$

Since the vectors are collinear

$\therefore a=kb.$

In other words coefficients of $\hat{i},\hat{j}$ and $\hat{k}$ are proportional.
$\therefore \frac{x}{1}=-\frac{3}{y}=\frac{7}{-z}$

$\therefore xy=-3,xz=-7$

$\therefore \frac{x{y}^2}{z}=\frac{x^2{y}^2}{xz}=\frac{{(-3)}^2}{-7}=-\frac{9}{7}$