Question

Q.1. find the image of the point having position vector i^ +3j^ +4k^ in the plane

r--> . (2i^ -j^+ k^) + 3 = 0.

Answer 1

The image of the point (3,5,2)

The point P having position vector i^ +3j^ +4k^ will be P(1,3,4).

Let Q (a,b,c) be the image of P(1,3,4) in the plane r--> (2i^ -j^+ k^) + 3 = 0.

the power of the point and its image w.r.t. the plane are equal and opposite.

2a-b+c+3 = - (2-3+4+3)

=> 2a-b+c = -9 ------(1)

PQ is perpendicular to the plane.Its equation can be written as -

=> a-1/2 = b-3/-1 = c-4/1 = t

=> a = 2t+1 , b = 3-t , c = t +4

Put the values of a, b and c in (1)

=> 2a-b+c = -9

=> 4t+2-3+t+t+4 = -9

=> 6t = -12

=> t = -2

a = 3 , b = 5 , c= 2

The image of point P on the plane is Q(3,5,2).