NDA2015MathematicsThree Dimensional GeometryActual
The lines 2 x=3 y=-z and 6 x=-y=-4 z
Options
- Aare perpendicular
- Bare parallel
- Cintersect at an angle 45^
- Dintersect at an angle 60^
Correct answer
A. are perpendicular
Step-by-step solution
2 x=3 y=-z or x 3 = y 2 = z -6 6 x=-y=-4 z or x 2 = y -12 = z -3 aligned & = x ₁ x ₂+ y ₁ y ₂+ z ₁ z ₂ x ₁^2+ y ₁^2+ z ₁^2 x ₂^2+ y ₂^2+ z ₃^2 & = (6-24+18) 3^2+3^2+(-6)^2 2^2+(-12)^2+(-3)^2 & =0 & =90^ aligned So lines are perpendicular