Practicing Success
The length of the perpendicular from the point (1, 2, 3) to the line $\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}$, is |
5 units 7 units 4 units none of these |
7 units |
Let L be the foot of the perpendicular drawn from the point P(1, 2, 3) to the given line. Let the coordinates of L be $(3λ + 6, 2λ + 7, -2λ + 7)$ ........(i) ∴ Direction ratios of PL are proportional to $3λ + 6 - 1, 2 λ + 7 - 2, - 2λ + 7 - 3$ i.e. $ 3λ + 5, 2λ + 5, -2λ + 4 $ Direction ratios of the given line are proportional to 3, 2, -2 Since PL is perpendicular to the given line. $∴3(3λ + 5) + 2(2λ + 5) + (-2) (-2λ + 4) = 0 ⇒ λ = - 1$ Putting λ = -1 in (i), we obtain that the coordinates of L as (3, 5, 9). $∴ PL = \sqrt{(3-1)^2 + (5-2)^2 + (9-3)^2}= 7 units$ |