COMEDK 2024 Shift 2 Paper

The direction ratios of the line joining R and Q are 2−0,−3−(−1),−1−3 i.e. 2,−2,−4. Hence, the equation of the line is given by:
‌

x−0

2

=‌

y−(−1)

−2

=‌

z−3

−4

=k
Let the foot of the perpendicular from P on the line be S(2k,−2k−1,−4k+3). Then, the direction ratios of PS are:
2k−1,−2k−9,−4k−1
Since PS is perpendicular to the line, the dot product of the direction ratios of PS and the line should be zero.
Solving the above equation, we get:
k=‌

−5

3

Therefore, the coordinates of S are:
‌S(‌

−10

3

,‌

7

3

,‌

29

3

)
Hence, the correct answer is Option C.