A plane P passes through the line of intersection of the planes `2x-y+3z=2,x+y-z=1` and the point (1,0,1).
What are the direction ratios of the line of intersection of the given planes ?

Options

A. `(: 2,-5,-3 :)`
B. `(:1,-5,-3:)`
C. `(:2,5,3:)`
D. `(:1,3,5:)`

Answer

A

Explanation

Tofind, intersection point first put z = 0
`2x-y=2`
`(x+y=1)/(3x=3)`
x = 1
`x+y=1`
`y=1-x`
At x -1, y = 0
`(x,y,z)-=(1,0,0)`
Putting x = 0
`y-z=1`
`(y+3z=2)/(2z=3)`
`z=3/2`
`y=1+z=1+3/2=5/2`
`(x,y,z)-=(0,5/2,3/2)`
Point of intersection `(x_1,y_1,z_1)-=(1,0,0)`
`(x_2,y_2,z_2)-=(0,5/2,3/2)`
Hence direction ratios of the line of intersection of given plane lt 2,-5,-3 gt