MHTCET 13 May 2023 Shift 2 Solved Paper

The given point is P(1,2,3).
and given line is r=(6

⋀

i

+7

⋀

j

+7t

⋀

k

)+λ(3

⋀

i

+2

⋀

j

−2

⋀

k

)
⇒‌‌‌

x−6

3

=‌

y−7

2

=‌

z−7

−2

=k (say)
So, any point on this line is given as Q(3k+6,2k+7,−2k+7)
Now, direction ratios of PQ are 3k+5,2k+5,−2k+4
Also, PQ⟂r
‌⇒‌‌3(3k+5)+2(2k+5)−2(−2k+4)=0
‌⇒‌‌17k+17=0⇒k=−1
Hence, foot of the perpendicular drawn on the given line is (3,5,9).