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JEE Main20248 Apr 2024Morning ShiftMathematicsThree Dimensional GeometryActual

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

Options

  1. A1- ^2 ^2
  2. B1- ^2 ^2
  3. C1+ ^2 ^2
  4. D1+ ^2 ^2

Correct answer

A. 1- ^2 ^2

Step-by-step solution

aligned & P ( x , y , z ), Q ( x , y , O ) ; x ^2+ y ^2+ z ^2= ^2 & OQ = x i + y j & = x x ^2+ y ^2 & = z x ^2+ y ^2+ z ^2 & ^2 = x ^2+ y ^2 x ^2+ y ^2+ z ^2 aligned distance of P from x -axis y ^2+ z ^2 aligned & ^2-x^2 1- x^2 ^2 & = 1- ^2 ^2 aligned

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