Let components of line segment vector be a , b , c ∴ a2+b2+c2 = (63)2 (i) Also
a
3
= −
b
2
=
c
6
= λ (say) ⇒ a = 3λ , b = - 2λ , c = 6λ From eq (i) 9λ2+4λ2+36λ2 = (63)2 ⇒ λ2+81 ⇒ λ = ± 9 since, a= 3λ < 0 as the line makes an obtuse angle with x - axis λ = - 9 ∴ Components are - 27 , 18 , - 54