Mark the correct alternative in the following:
The image of the point (1, 3, 4) in the plane 2x – y + z + 3 = 0 is
We know, if the image of a point P (x0, y0, z0) on a plane Ax + By + Cz + D=0……… (1) is Q (x1, y1, z1) then,
The given plane is, 2x–y + z + 3=0 …………. (2)
Comparing equation (2) with equation (1) we get,
A=2, B= - 1, C=1, D=3
And, here x0=1, y0=3, z0=4
So,
x_1=(2⨯( - 2)) + 1
= - 4 + 1
x_1= - 3,
y_1=(( - 1)⨯( - 2)) + 3
=2 + 3
y_1=5 and
z_1=(1⨯( - 2)) + 4
= - 2 + 4
z_1=2
So, the image of the point (1, 3, 4) in the plane 2x – y + z + 3 = 0 is ( - 3, 5, 2)