Question

The length of the perpendicular from the point (2, –1, 4) on the straight line `(x + 3)/10 = ("y" - 2)/(-7) = "z"/1`, is ______.

पर्याय

• greater than 2 but less than 3

• less than 2

• greater than 4

• greater than 3 but less than 4

Answer 1

The length of the perpendicular from the point (2, –1, 4) on the straight line `(x + 3)/10 = ("y" - 2)/(-7) = "z"/1`, is greater than 3 but less than 4.

Explanation:

From (2, –1, 4)

Any point of the line

`(x + 3)/10 = ("y" - 2)/(-7) = "z"/1` = λ

x = 10λ – 3, y = –7λ + 2, z = λ

AB and line are ⊥

D'r of AB 10λ –3 –2, –7λ + 2 + 1, λ – 4

10(10λ – 5) + (–7)(–7λ + 3) + 1(λ – 4) = 0

 λ = `1/2`

Point `(10 xx 1/2 -3),(-7 xx 1/2  + 2), 1/2 = (2, (-3)/2, 1/2)`

Distance = `sqrt((2 - 2)^2 + (3/2 + 1)^2 + (4 - 1/2)^2` ≈ 3.57