The distance of the point P(x, y, z) from the | vedclass

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

Question

(A) In a three-dimensional Cartesian coordinate system,the position of a point $P$ is given by its coordinates $(x, y, z)$.The $yz$-plane is defined b

Vedclass · Accepted Answer

$|x|$

Vedclass · Answer

(A) In a three-dimensional Cartesian coordinate system,the position of a point $P$ is given by its coordinates $(x, y, z)$.The $yz$-plane is defined by the equation $x = 0$.The perpendicular distance of any point $(x, y, z)$ from the plane $ax + by + cz + d = 0$ is given by the formula $d = \frac{|ax_0 + by_0 + cz_0 + d|}{\sqrt{a^2 + b^2 + c^2}}$.For the $yz$-plane,the equation is $1x + 0y + 0z + 0 = 0$.Substituting the coordinates of point $P(x, y, z)$ into the distance formula:$d = \frac{|1(x) + 0(y) + 0(z) + 0|}{\sqrt{1^2 + 0^2 + 0^2}}$$d = \frac{|x|}{1} = |x|$.Thus,the distance of the point $P(x, y, z)$ from the $yz$-plane is $|x|$.

The distance of the point $P(x, y, z)$ from the $yz$-plane is:

Similar Questions

If the centroid of the tetrahedron $OABC$,where $O$ is the origin $(0, 0, 0)$ and $A, B, C$ are given by $(a, 2, 3)$,$(1, b, 2)$,and $(2, 1, c)$ respectively,is $(1, 2, -1)$,then the distance of point $P(a, b, c)$ from the origin is equal to:

The distance between the points $(1, 3, 2)$ and $(2, 1, 3)$ is:

The perpendicular distance of the point $(3, 4, 5)$ from the $y$-axis is

The coordinates of points $A, B, C, D$ are $(a, 2, 1), (1, -1, 1), (2, -3, 4)$ and $(a+1, a+2, a+3)$ respectively. If $AB = 5$ and $CD = 6$,then $a = $

Locate the following points in a three-dimensional Cartesian coordinate system:
$(i)$ $(1, -1, 3)$
$(ii)$ $(-1, 2, 4)$
$(iii)$ $(-2, -4, -7)$
$(iv)$ $(-4, 2, -5)$

Vedclass Test Series

Exam Paper Generator

Online Exam Module