Home
Class 12
MATHS
If the point (2 , alpha , beta) lies on...

If the point `(2 , alpha , beta) ` lies on the plane which passes through the points `(3,4,2) and (7,0,6)` and is perpendicular to the plane `2x-5y=15,` then `2 alpha - 3 beta` is equal to:

A

17

B

7

C

12

D

5

Text Solution

Verified by Experts

The correct Answer is:
B
Normal vector of plane passing through `(2, alpha , beta ), (2,4,2) and (7,0,6)` is
`vecn = |{:(hati, hatj, hatk),(-5, alpha, beta -6),(4,-4, 4):}|therefore " " vecn = hati ( 4 alpha - 4 beta -24) + hatj(4 beta-24)+ hatk (20-4 alpha )`
`therefore` This plane is perpendicular `o 2x -5y =15therefore` Dot product of their normal is 0.
`implies 2 (4 alpha + 4 beta -24) -5(4 beta -4) implies 8 alpha -12 beta =28 and 2 alpha - 3 beta =7.`
Promotional Banner

Similar Questions

Explore conceptually related problems

The equation of the plane passing through the points (0,1,2) and (-1,0,3) and perpendicular to the plane 2x+3y+z=5 is

The equation of the plane which passes through the points (2, 1, -1) and (-1, 3, 4) and perpendicular to the plane x- 2y + 4z = 0 is

Find the equation of the plane through the points A(3,4,2) and B(7,0,6) and perpendicular to the plane 2x-5y=15 . Hint: The given plane is 2x-5y+0z=15 .

The line passing through the point -1, 2, 3 and perpendicular to the plane x - 2y + 3z + 5 = 0 will be

Consider the plane passing through the points A(2,2,1),B(3,4,2) and C(7,0,6) Which one of the following points lies on the plane

Find the equation of a plane which passes through the point (1,2,3) and which is equally inclined to the planes x-2y+2z-3=0 and 8x-4y+z-7=0

I If a point (alpha,beta) lies on the circle x^(2)+y^(2)=1 then the locus of the point (3 alpha.+2,beta), is

Find the equation of a plane passing through the point (2,-1,5), perpendicular to the plane x+2y-3z=7 and parallel to the linne (x+5)/3=(y+1)/-1=(z-2)/1 .