A line segment has length 63 and direction ratios are 3,-2,6 . If...

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 \lt 0) as the line makes an obtuse angle with $x$-axis, (\lambda=-9) and the required components are $-27,18,-54$.