MHTCET 2016 Math Solved Paper

(a) Coordinates of points A and B are given as (6,-4,4) and (0,0, - 4) and coordinates of points C and D are given as (-1, -2, -3) and (1,2, -5). Now, equation of line which passes through (0, 0 ,-4 ) and (6,-4,4) is

x−0

6

=

y−0

−4

=

z+4

4+4

=k[Let]
⇒ x = 6k,y = - 4k and z = 8k - 4 ...(i)
The equation of line which passes through ( - 1 , - 2 , - 3 ) and(1 , 2, -5) is

x+1

1+1

=

y+2

2+2

=

z+3

−5+3

⇒

x+1

2

=

y+2

4

=

3+3

−2

....(ii)
As, two lines intersect,so point (6k, -4k, 8k - 4) satisfy eq. (ii), we get

6k+1

2

=

−4k+2

4

=

8k−4+3

−2

⇒ 6k + 1 = -2k + 1 = - (8 k - 1)
⇒ 6k + 1 = - 2k + 1 ⇒ 8k = 0
⇒ k = 0
∴ x = 6 x 0 , y = - 4 × 0 and z = 8 x 0 - 4
⇒ x = 0, y = 0 and z = 4
This is equal to the B coordinate.