(D) In a three-dimensional Cartesian coordinate system,any point in space is represented by the coordinates $(x, y, z)$.For any point lying on the $x$

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(D) In a three-dimensional Cartesian coordinate system,any point in space is represented by the coordinates $(x, y, z)$.For any point lying on the $x$-axis,the distance from the $xy$-plane and the $xz$-plane is zero.This means that both the $y$-coordinate and the $z$-coordinate must be equal to $0$.Therefore,the coordinates of any point on the $x$-axis are of the form $(x, 0, 0)$,which implies $y = 0$ and $z = 0$.

Class 12 Mathematics THREE DIMENSIONAL GEOMETRY System of co-ordinates, Direction cosines and direction ratios, Projection

Easy

All the points on the $x$-axis have

A
$x = 0$
B
$y = 0$
C
$x = 0, y = 0$
D
$y = 0, z = 0$

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THREE DIMENSIONAL GEOMETRY

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System of co-ordinates, Direction cosines and direction ratios, Projection

The angle between the lines whose direction ratios satisfy the equations $l+m+n=0$ and $l^2=m^2+n^2$ is

DifficultAP EAMCET 2014

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If a line makes angles $\alpha, \beta, \gamma$ with the coordinate axes,then $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = \dots$

Medium

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$A$ line passes through the points $A (6, -7, -1)$ and $B (2, -3, 1)$. Find the direction cosines of the line such that the angle $\alpha$ made with the $x$-axis is acute.

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Find a vector $\vec{r}$ of magnitude $3 \sqrt{2}$ units which makes an angle of $\frac{\pi}{4}$ and $\frac{\pi}{2}$ with $y$ and $z$-axes,respectively.

Medium

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If the direction cosines of a line are $\left(\frac{a}{\sqrt{83}}, \frac{5}{\sqrt{83}}, \frac{c}{\sqrt{83}}\right)$ and $c-a=4$,then $ca=$

EasyAP EAMCET 2022

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All the points on the $x$-axis have

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The angle between the lines whose direction ratios satisfy the equations $l+m+n=0$ and $l^2=m^2+n^2$ is

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