Equation of a line in the plane `pi-=2x-y+z-4=0` which is perpendicular to the line `l` whse equation is `(x-2)/1=(y-2)/(-1)=(z-3)/(-2)` and which passes through the point of intersection of `l and pi` is

Options

A. `(x-2)/(1)=(y-1)/(5)=(z-1)/(-1)`
B. `(x-1)/(3)=(y-3)/(5)=(z-1)/(-5)`
C. `(x+2)/(2)=(y+1)/(-1)=(z+1)/(1)`
D. `(x-2)/(2)=(y-1)/(-1)=(z-1)/(1)`

Answer

B

Explanation

Let direction ratios of the line be (a,b,c), then
and `a-b-2c=0,i.e.,(a)/(3)=(b)/(5)=(c)/(-1)`
Therefore, direction ratios of the line are (3,5,-1). Any point on the given line is `(2+lamda,2-lamda,3-2lamda),` it lies on the given plane `pi` if
`2(2+lamda)-(2-lamda)+(3-2lamda)=4`
or `4+2lamda-2+lamda+3-2lamda=0orlamda=-1`
Therefore, the point of intersection of the line and the plane is (1,3,5).
Therefore, equation of the required line is
`(x-1)/(3)=(y-3)/(5)=(z-5)/(-1)`