Question

A line segment has length 63 and direction ratios, <3, -2, 6>. If the line makes an obtuse angle with x-axis, then the components of the line vector are

• A. 27, -18, 54
• B. -27, 18, -58
• C. -27, 18, -54
• D. 27, -18, -54

Answer 1

Answer: (C)

Let the components of the line segment vector be $a,b,c,$ then
$a^2+b^2+c^2=(63{)}^2$ ...(1)
Also $\frac{a}{3}=\frac{b}{-2}=\frac{c}{6}=\lambda$ (say) then $a=3\lambda ,b=-2\lambda$ and $c=6\lambda$. and from (1) , we have
$9{\lambda }^2+4{\lambda }^2+36{\lambda }^2=(63{)}^2\Rightarrow 49{\lambda }^2=(63{)}^2$
$\lambda =\pm \frac{63}{7}=\pm 9$.
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.