Mathematics - Probability Question with Solution | TestHub

Let the components of the line vector be a, b, c. Then ${\mathrm{a}}^2+{\mathrm{b}}^2+{\mathrm{c}}^2=(63{)}^2$ ...(i) Also $\frac{\mathrm{a}}{3}=\frac{\mathrm{b}}{-2}=\frac{\mathrm{c}}{6}=\lambda$ (say), then $\mathrm{a}=3\lambda$, $\mathrm{b}=-2\lambda$ and $\mathrm{c}=6\lambda$ and from (i) we have $9{\lambda }^2+4{\lambda }^2+36{\lambda }^2=(63{)}^2$ $\Rightarrow 49{\lambda }^2=(63{)}^2$ $\Rightarrow \lambda =\pm \frac{63}{7}=\pm 9$ Since $a=3\lambda <0$ as the line makes an obtuse angle with $x$-axis, $\lambda =-9$ and the required components are $-27,18,-54$.