(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 $x$

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(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
$y = 0, z = 0$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Three Dimensional Geometry

Subtopic

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

If the projections of a line segment on the coordinate axes are $2, 3, 6$,find the length of the line segment.

Easy

View Solution

Find the direction cosines of the sides of the triangle whose vertices are $(3,5,-4), (-1,1,2)$ and $(-5,-5,-2)$.

Medium

View Solution

The number of straight lines that are equally inclined to the three-dimensional coordinate axes is

Easy

View Solution

If a line in space makes angles $\alpha, \beta$,and $\gamma$ with the coordinate axes,then $\cos 2\alpha + \cos 2\beta + \cos 2\gamma + \sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma$ equals:

MediumTS EAMCET 2009

View Solution

If a vector $\vec{r}$ with direction cosines $l, m, n$ is equally inclined to the coordinate axes, then the total number of such vectors is

MediumMHT CET 2017

View Solution

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

All the points on the $x$-axis have

Similar Questions

If the projections of a line segment on the coordinate axes are $2, 3, 6$,find the length of the line segment.

Find the direction cosines of the sides of the triangle whose vertices are $(3,5,-4), (-1,1,2)$ and $(-5,-5,-2)$.

The number of straight lines that are equally inclined to the three-dimensional coordinate axes is

If a line in space makes angles $\alpha, \beta$,and $\gamma$ with the coordinate axes,then $\cos 2\alpha + \cos 2\beta + \cos 2\gamma + \sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma$ equals:

If a vector $\vec{r}$ with direction cosines $l, m, n$ is equally inclined to the coordinate axes, then the total number of such vectors is

Vedclass Test Series

Exam Paper Generator

Online Exam Module