JEE Advanced Model Paper 19 with solutions for online practice

The projection will be the line of intersection of the given plane, with the plane containing the givenline and a lie ⊥ to the given plane.
Plane containing the given line is a(x – 1) + b(y + 1) + c(z – 3) = 0.
Where 2a – b + 4c = 0. This will be ⊥ given plane if a + 2b + c = 0 on solving

a

−4

=

b

2

=

c

5

∴ The equation of the plane is 9x – 2y – 5z + 4 = 0.
∴ The line is the line of intersection of (1) and x + 2y + z – 12 = 0. Let l, m, n be the d.cs of the line.
Then 9l – 2m – 5n = 0 and l + 2m + n = 0.
→

l

4

=

m

−7

=

n

10

Substituting y = 0, any point on the line is (4, 0, 8).
∴ Equation is

x−4

4

=

y

−7

=

z−8

10