CBSE Class 12-science Answered
Answer : Let P (0, 2, 3) be the point whose image is to be determined.
Draw perpendicular from P to the given line which cuts the line L, which is its foot of perpendicular.
Then, image of P will be in the downward direction and at the same distance from L as P.
Let P' (x 1, y 1, z 1) be the image of point P. Then we will find the values of x 1, y 1, z 1.
Then,
Given line is
=> (x+3) / 5 = (y-1)/2 = (z+4)/3 =t (let)
=> x = 5t -3 , y = 2t+1 , z= 3t - 4
i.e., the co-ordinate of any general point which lies on the given line is ( 5t -3 , 2t+1 , 3t - 4).
? Co-ordinate of L are ( 5t -3 , 2t+1 , 3t - 4).
Now,
Direction ratio's of PL will be
5t -3 -0 , 2t+1-2 , 3t - 4-3
= 5t - 3 , 2t -1 , 3t-7
Also,
Direction ratio's of given line are 5, 2, 3.
But, PL is perpendicular to the given line.
=> 5(5t - 3) +2( 2t -1 ) +3 ( 3t-7) =0
=> 38t = 38
=> t = 1
? Co-ordinate of L are (2, 3, -1)
Now,
L is the mid point of PP',
By mid point formula
=> (0 + x1 )/2 = 2 , (2+ y1)/2 =3 , (3+ z1)/2 = -1
=> x1 = 4 , y1 =4 , z1 = -5
Hence, the image of (0, 2, 3) is (4, 4, -5).