Question

The equation of line passing through (3, -1, 2) and perpendicular to the lines `overline("r")=(hat"i"+hat"j"-hat"k")+lambda(2hat"i"-2hat"j"+hat"k")` and `overline("r")=(2hat"i"+hat"j"-3hat"k")+mu(hat"i"-2hat"j"+2hat"k")` is ______.

Options

• `(x+3)/2=(y+1)/3=(z-2)/2`

• `(x-3)/3=(y+1)/2=(z-2)/2`

• `(x-3)/2=(y+1)/3=(z-2)/2`

• `(x-3)/2=(y+1)/2=(z-2)/3`

Answer 1

The equation of line passing through (3, -1, 2) and perpendicular to the lines `overline("r")=(hat"i"+hat"j"-hat"k")+lambda(2hat"i"-2hat"j"+hat"k")` and `overline("r")=(2hat"i"+hat"j"-3hat"k")+mu(hat"i"-2hat"j"+2hat"k")` is `underline((x-3)/2=(y+1)/3=(z-2)/2)`.

Explanation:

Let a, b, c be the d.r.s. of the required line d.r.s. of the given lines are 2, -2, 1 and 1, -2, 2.

∴ 2a - 2b + c = 0    ....(i)

a - 2b + 2c = 0     ....(ii)

`therefore a/(-4+2)=(-b)/(4-1)=c/(-4+2)`

`=>a/-2=b/-3=c/-2`

∴ Equation of the required line is

`(x-3)/-2=(y+1)/-3=(z-2)/-2`

`=>(x-3)/2=(y+1)/3=(z-2)/2`