The image of the point $(3, 2, 1)$ in the plane $2x-y+3z = 7$ is
- (1, 2, 3)
- (2, 3, 1)
- (3, 2, 1)
- (2, 1, 3)
The Correct Option is C
Solution and Explanation
$\frac{x - x_{1}}{a} = \frac{y - y_{1}}{b} -= \frac{z- z_{1}}{c} $
$ = \frac{ -2 ax_{1 } + by_{1} +cz_{1} + d}{a^{2} + b^{2} +c^{2}}$
Here, point is $(3, 2, 1)$ and plane is $2x - y + 3z = 7$.
$ \therefore \, \, \frac{x-2}{2} = \frac{y- 2}{-1} = \frac{z - 1}{ 3 }$
$ = \frac{-2 2 3 - 2 + 3 1 - 7}{2^{2} + 1^{2} + 3^{2}}$
$ \Rightarrow \frac{x-3}{2} = \frac{y -2}{-1} = \frac{z-1}{3} = -20$
$ \Rightarrow x = 3 , y =2 ,z =1 $
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Concepts Used:
Coordinates of a Point in Space
Three-dimensional space is also named 3-space or tri-dimensional space.
It is a geometric setting that carries three values needed to set the position of an element. In Mathematics and Physics, a sequence of ‘n’ numbers can be acknowledged as a location in ‘n-dimensional space’. When n = 3 it is named a three-dimensional Euclidean space.
The Distance Formula Between the Two Points in Three Dimension is as follows;
The distance between two points P1 and P2 are (x1, y1) and (x2, y2) respectively in the XY-plane is expressed by the distance formula,
Read More: Coordinates of a Point in Three Dimensions