Question

The direction ratios of the line which is perpendicular to the two lines `(x - 1)/2 = ("y" - 1)/(-2) = ("z + 1")/1 and (x - 2)/1 = ("y - 1")/(- 2) = ("z + 3")/2` are ______.

Options

• 2, 3, 2

• 2, -3, 2

• 2, 3, -5

• -1, 2, 2

Answer 1

The direction ratios of the line which is perpendicular to the two lines `(x - 1)/2 = ("y" - 1)/(-2) = ("z + 1")/1 and (x - 2)/1 = ("y - 1")/(- 2) = ("z + 3")/2` are 2, 3, 2.

Explanation:

Let a, b, c be the direction ratios of the line which is perpendicular to `(x - 1)/2 = ("y" - 1)/(-2) = ("z + 1")/1 and (x - 2)/1 = ("y - 1")/(- 2) = ("z + 3")/2`

∴ 2a - 2b + c = 0   ...(i)

a - 2b + 2c = 0   ...(ii)

Solving (i) and (ii), we get

`"a"/(|(-2,1),(-2,2)|) = (-"b")/(|(2,1),(1,2)|) = "c"/(|(2,-2),(1,-2)|)`

`=> "a"/(-2) = (-"b")/3 = "c"/(-2)`

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

⇒ a = 2, b = 3 and c = 2