CGPET 2019 Solved Paper

The given line l is

x+5

1

=

y+3

4

=

z−6

−9

Any point Q on the line l is given by
⇒

x+5

1

=

y+3

4

=

z−6

−9

=λ
⇒x=λ−5,y=4λ−3,z=−9λ+6
Direction ratios of PQ are
λ−5−24λ−3−4,−9λ+6+1
or λ−7,4λ−7,−9λ+7Since, PQ⊥L
∴(λ−7)+4(4λ−7)−9(−9λ+7)=0
⇒λ−7+16λ−28+81λ−63=0
⇒98λ=98⇒λ=1
∴ Coordinates of Q are (1−5,4−3,−9+6)
i.e., (−4,1,−3)
Now, Required distance
=√(2+4)2+(4−1)2+(−1+3)2
=√36+9+4=√49=7 unit.