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

  • A
    $\gamma \sqrt{1-\sin^2 \phi \cos^2 \theta}$
  • B
    $\gamma \sqrt{1+\cos^2 \theta \sin^2 \phi}$
  • C
    $\gamma \sqrt{1-\sin^2 \theta \sin^2 \phi}$
  • D
    $\gamma \sqrt{1+\cos^2 \phi \sin^2 \theta}$

Explore More

Similar Questions

If a line makes an angle of $30^{\circ}, 60^{\circ}, 90^{\circ}$ with the positive direction of $x, y, z$-axes,respectively,then find its direction cosines.

If the direction cosines of two lines are such that $2l + m + 2n = 0$ and $3l^2 + 5m^2 - 11n^2 = 0$,then the angle between the two lines is

The direction cosines of the line passing through $P(2, 3, -1)$ and the origin $O(0, 0, 0)$ are:

If the direction cosines of two lines are given by $l+3m+5n=0$ and $5lm-2mn+6ln=0$, then the angle between the lines is

If the direction ratios of a line are $1, -3, 2$,then the direction cosines of the line are

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo