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

Step-by-step solution

Let the components of the line vector be a, b, c. Then ( a ^2+ b ^2+ c ^2=(63)^2 ) ...(i) Also ( a 3 = b -2 = c 6 = ) (say), then ( a =3 ), ( b =-2 ) and ( c =6 ) and from (i) we have (9 ^2+4 ^2+36 ^2=(63)^2 ) ( 49 ^2=(63)^2 ) ( = 63 7 = 9 ) Since (a=3 < 0 ) as the line makes an obtuse angle with (x )-axis, ( =-9 ) and the required components are (-27,18,-54 ).