Match the following Column I to Column II

Answer

`a to q; b to r; c to s; d to p`

Explanation

If the required image is `(x, y, z)`, then `(x-3)/(2)= (y-5)/(1) = (z-7)/(1)= - (2(6+5+7+18))/(2^(2)+1^(2)+1^(2))= -12`
or `(-21, -7, -5)`.
b. Any point on the line `(x-2)/(-3)=(y-1)/(2)= (z-3)/(2)= lamda` is `(-3lamda+2, 2lamda+1, 2lamda+3)`, which lies on plane `2x+y-z=3`. Therefore,
`" "-6lamda+4+2lamda+1-2lamda-3=3`
`" "-6lamda=1`
`lamda= -1//6`
Therefore, the point is `((5)/(2), (2)/(3),(8)/(3))`.
c. If `(x, y, z)` is the required foot of the perpendicular, then `(x-1)/(2)= (y-1)/(-2)= (z-2)/(4) = - ((2-2+8+5))/(2^(2)+ (-2)^(2)+ 4^(2))`
or `" "(x, y, z)-= ((-1)/(12), (25)/(12), (-2)/(12))`
d. Any point on the line `(x-1)/(2)= (y-2)/(3)= (z-3)/(4)= lamda` is `P(2lamda+1, 3lamda+2, 4lamda+3)`, which satisfies the line `(x-4)/(5)= (y-1)/(2)= (z)/(1)`
or `" "(2lamda+1-4)/(5)= (3lamda+2-1)/(2)= (4lamda+3)/(1)`
or `" "lamda= -1`
The required point is `(-1, -1, -1)`