Math, asked by waquasali5043, 4 months ago

The reflection of the points (3, 1, 2) in the plane
x + 2y + z = 1 is:​

Answers

Answered by jkrishn315
0

Answer:

wrong question please send proper question

Step-by-step explanation:

please

Answered by sonuvuce
0

The reflection of the point (3, 1, 2) in the plane x + 2y + z = 1 is (1, -3, 0)

Step-by-step explanation:

Given:

The equation of the plane

x + 2y + z = 1

And the point (3, 1, 2)

To find out:

The reflection of point (3, 1, 2) in the plane

Solution:

The equation of plane is : x + 2y + z = 1

The vector normal to the plane will be (1, 2, 1)

Now a  line perpendicular to the given plane and passing through the point (3, 1, 2) can be written as

\frac{x-3}{1}=\frac{y-1}{2}=\frac{z-2}{1}

Let \frac{x-3}{1}=\frac{y-1}{2}=\frac{z-2}{1}=\lambda

Any point lying on the line will be (\lambda+3, 2\lambda+1, \lambda+2)

To find the point where this line meets the plane:

The point will satisfy the equation of the plane

Therefore,

\lambda+3+2(2\lambda+1)+\lambda+2=1

6\lambda+7=1

\implies \lambda=-\frac{6}{6}=-1

Therefore, the coordinate of the point where line meets the plane is

(2, -1, 1)

This point will be the mid point of the given point (3, 1, 2) and the reflection point

If the coordinate of reflection points are (x', y', z') then

\frac{x'+3}{2}=2\implies x'=1

\frac{y'+1}{2}=-1\implies y'=-3

\frac{z'+2}{2}=1\implies z'=0

Therefore, the reflection of the point (3, 1, 2) is (1, -3, 0)

Hope this answer is helpful.

Know More:

Q: 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.

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