MHT CET 2017 Math Solved Paper

(a) The coordinates of given point is (2,3, λ ).
So, equation of the plane is

→

r

⋅(3

^

i

+2

^

j

+6

^

k

) = 13
⇒ (x

^

i

+y

^

j

+z

^

k

) ⋅ (3

^

i

+2

^

j

+6

^

k

) = 13
3x + 2y + 6z - 13 = 0
Therefore, distanceof the plane from the given point (2,3, λ ) will be
|

3×2+2×3+6×λ−13

√32+22+62

| = 5 [Given]
⇒ ± 5=

6λ−1

√49

> ±35 = 6 λ -1
⇒ 35 = 6 λ -1 or - 35 = 6 λ -1
Hence, λ = 6, -

17

3