Question

The angle between the lines `2x=3y=-z and 6x=-y=-4z` is (A) `0^0` (B) `90^0` (C) `45^0` (D) `30^0`
A. are perpendicular
B. are parallel
C. intersect at an angle `45^(@)`
D. intersect at an angle `60^(@)`

Answer 1

Correct Answer - A
`2x=3y=-z`
or `x/3=y/2=z/(-6)`
`6x=-y=-4z`
or `x/2=y/(-12)=z/(-3)`
`cos theta=(x_(1)x_(2)+y_(1)y_(2)+z_(1)z_(2))/(sqrt(x_(1)^(2)+y_(1)^(2)+z_(1)^(2)).sqrt(x_(2)^(2)+y_(2)^(2)+z_(3)^(2)))`
`=((6-24+18))/(sqrt(3^(2)+2^(2)+(-6)^(2)).sqrt(2^(2)+(-12)^(2)+(-3)^(2)))`
`cos theta=0`
`theta=90^(@)`
So lines are perpendicular