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)

-27, 18, -54

Answer 2

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.