Let P ( x , y , z ) be a point in the first octant, whose projection in the x y -plane is the point Q . Let OP = γ ; the angle between OQ and the positive x -axis be θ ; and the angle between OP and t

Question

Let P ( x , y , z ) be a point in the first octant, whose projection in the x y -plane is the point Q . Let OP = γ ; the angle between OQ and the positive x -axis be θ ; and the angle between OP and the positive z -axis be ϕ , where O is the origin. Then the distance of P from the x -axis is

TestHub · Accepted Answer

​ P ( x , y , z ) , Q ( x , y , O ) ; x 2 + y 2 + z 2 = γ 2 OQ ​ = x i ^ + y j ^ ​ cos θ = x 2 + y 2 ​ x ​ cos ϕ = x 2 + y 2 + z 2 ​ z ​ ⇒ sin 2 ϕ = x 2 + y 2 + z 2 x 2 + y 2 ​ ​ distance of P from x -axis y 2 + z 2 ​ ​ ⇒ γ 2 − x 2 ​ ⇒ γ 1 − γ 2 x 2 ​ ​ = γ 1 − cos 2 θ sin 2 ϕ ​ ​

Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Options:

Doubts & Discussion