Practicing Success
The foot of perpendicular from point (2, 4, -1) on the line $\frac{x+5}{1}=\frac{y+3}{4}=\frac{z-6}{-9}$ is: |
(-4, 1, -3) (4, 1, -3) (4, 1, 3) (4, -1, 3) |
(-4, 1, -3) |
$\frac{x+5}{1}=\frac{y+3}{4}=\frac{z-6}{-9}=λ$ DR = (1, 4, -9) $x=λ-5,y=4λ-3,z=-9λ+6$ Q ⇒ (a, b, c) = $(λ−5,4λ−3,-9λ+6)$ ...(i) DR's of PQ = $(λ−5-2,4λ−3-4,-9λ+6+1)$ $=(λ−7,4λ−7,-9λ+7)$ (DR's of PQ).(DR's of line) = 0 $((λ−7).1+(4λ−7).4-9((-9λ)+7))=0$ $λ−7+16λ-28+81λ-63=0$ $98λ-98=0⇒98λ=98⇒λ=\frac{98}{98}=1$ ...(ii) Putting eq. (ii) in (i) $((1)−5,4(1)−3,-9(1)+6)$ $⇒(-4, 1, -3)$ |