Question

The coordinates of the foot of perpendicular from (2, –1, 5) to the line `(x - 11)/10 = (y + 2)/(-4) = (z + 8)/(-11)` are ______.

पर्याय

• (0, 2, 3)

• (1, 2, 3)

• (2, 1, 3)

• (1, 3, 2)

Answer 1

The coordinates of the foot of perpendicular from (2, –1, 5) to the line `(x - 11)/10 = (y + 2)/(-4) = (z + 8)/(-11)` are (1, 2, 3).

Explanation:

Let M be the foot of the perpendicular drawn from the point P(2, –1, 5) to the line `(x - 11)/10 = (y + 2)/(-4) = (z + 8)/(-11)`

Let  `(x - 11)/10 = (y + 2)/(-4) = lambda`

∴ The co-ordinates of any point on the line are

M ≡ `(10lambda + 11, -4lambda - 2, - 11lambda - 8)` ......(i)

∴ The direction ratios of PM are

`10lambda + 9, -4lambda - 1, 11lambda - 13`

Direction ratios of given line are `10, -4, -11`

Since PM is perpendicular to the given line,

`10(10lambda + 9) -4(-4lambda - 1) -11(-11lambda - 13)` = 0

⇒ `100lambda + 90 + 16lambda + 4 + 121lambda + 143` = 0

⇒ `lambda = -1`

∴ M ≡ (1, 2, 3)   ......[From (i)]