Q. 265.0( 1 Vote )
Find the image of the point (2, -1, 5) in the line
Answer :
Given: Point (2, -1, 5)
Equation of line 
The equation of line can be re-arranged as 
The general point on this line is
(10r + 11, -4r – 2, -11r – 8)
Let N be the foot of the perpendicular drawn from the point P(2, 1, -5) on the given line.
Then, this point is N(10r + 11, -4r – 2, -11r – 8) for some fixed value of r.
D.r.’s of PN are (10r + 9, -4r - 3, -11r - 3)
D.r.’s of the given line is 10, -4, -11.
Since, PN is perpendicular to the given line, we have,
10(10r + 9) – 4(-4r – 3) – 11(-11r – 3) = 0
100r + 90 + 16r + 12 + 121r + 33 = 0
237r = 135
r 
Then, the image of the point is
Therefore, the image is (0, 5, 1).
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Find the vector and Cartesian equations of the line through the point (1, 2, -4) and perpendicular to the two lines.
and 
Write the vector equations of the following lines and hence determine the distance between them:
