Question

If the line `(x - 3)/2 = (y + 2)/-1 = (z + 4)/3` lies in the plane lx + my - z = 9, then l² + m² is equal to ______

पर्याय

• 18

• 5

• 2

• 26

Answer 1

If the line `(x - 3)/2 = (y + 2)/-1 = (z + 4)/3` lies in the plane lx + my - z = 9, then l² + m² is equal to 2.

Explanation:

Line is perpendicular to normal of plane

⇒ `(2hati - hatj + 3hatk).(lhati + mhatj - hatk) = 0`

⇒ 2l - m - 3 = 0 ..................(i)

(3, -2, -4) lies on the plane lx + my - z = 9

∴ 3l - 2m + 4 = 9

⇒ 3l - 2m = 5 .................(ii)

Solving (i) and (ii), we get

l = 1, m = -1

∴ `l^2 + m^2 = 2`