Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Model Papers
0 votes

Prove that the image of the point (3,-2,1) in the plane \( 3x-y+4z=2\) lies on the plane \( x+y+z+4=0\).

Can you answer this question?

1 Answer

0 votes
  • Mid point of AB where $A(x_1,y_1,z_1)\:and\:B(x_2,y_2,z_2)$ is given by $\bigg(\large\frac{x_1+x_2}{2},\frac{y_1+y_2}{2},\frac{z_1+z_2}{2}\bigg)$
Step 1:
Equation of the given plane is $3x-y+4z=2$----(1)
Let $P(3,-2,1)$ have image as $P'(x_1,y_1,z_1)$
Thus PP' is $\perp$ to the plane (1)
Let $M$ be the mid point of PP' and lie on th plane (1)
Equation of the line PP' is
Any point P' on it is $(3k+3,-k-2,4k+1)$
Since this point lies on the plane
$\therefore k=-\large\frac{1}{2}$
Step 2:
Now substituting the value of k we get the coordinate of M as
$\Rightarrow (\large\frac{3}{2},-\frac{3}{2}$$,-1)$
Since M is the mid point of PP'
$\Rightarrow x_1=0$
$\Rightarrow y_1=-1$
Step 3:
Hence the coordinates of M are (0,-1,-3)
Now substituting for $x,y$ and $z$ in the equation
$\Rightarrow 0-1-3+4=0$
Hence the image of the point $(3,-2,1)$ in the plane $3x-y+4z=2$ lies on the plane.
answered Nov 8, 2013 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App