A) 27, -18, 54
B) 27,18, - 54
C) - 27,18, - 54
D) 27, -18, - 54
Correct Answer: C
Solution :
Let components of line segment vector be a, b, c. \[\therefore \]\[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}={{(63)}^{2}}\] ?(i) Also, \[\frac{a}{3}=-\frac{b}{2}=\frac{c}{6}=\lambda \] (say) \[\Rightarrow \]\[a=3\lambda ,b=-2\lambda ,c=6\lambda \] From Eq. (i), \[9{{\lambda }^{2}}+4{{\lambda }^{2}}+36{{\lambda }^{2}}={{(63)}^{2}}\] \[\Rightarrow \]\[{{\lambda }^{2}}+81\Rightarrow \lambda =\pm 9\] Since, \[a=3\lambda <0\]as the line makes an obtuse angle with x-axis, \[\lambda =-9\]. \[\therefore \] Components are - 27,18, - 54.
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