If the image of the point P(1, -2, 3) in the plane, 2x + 3y - 4z + 22 = 0 measured parallel to the line, (x/1) = (y/4) = (z/5) is Q, then PQ is equal to :

Question

If the image of the point P(1, -2, 3) in the plane, 2x + 3y - 4z + 22 = 0 measured parallel to the line, (x/1) = (y/4) = (z/5) is Q, then PQ is equal to : (A) 2 √42 (B)  √42 (C) 6 √5 (D) 3 √5

Tardigrade Admin · Accepted Answer

Equation of PQ, (x-1/1)=(y+ 2/4)=(z-3/5) Let M be (λ+1,4λ-2,5λ+3) As it lies on 2x + 3y - 4z + 22 = 0 λ=1 For Q, λ = 2 Distance PQ=2√12+42+52=2√42

Q. If the image of the point $P (1, - 2, 3)$ in the plane, $2 x + 3 y - 4 z + 22 = 0$ measured parallel to the line, $\frac{x}{1} = \frac{y}{4} = \frac{z}{5}$ is $Q$ , then $PQ$ is equal to :

$242$

$42$

$65$

$35$

Equation of PQ, $\frac{x - 1}{1} = \frac{y + 2}{4} = \frac{z - 3}{5}$
Let M be $(λ + 1, 4 λ - 2, 5 λ + 3)$
As it lies on $2 x + 3 y - 4 z + 22 = 0$
$λ = 1$
For $Q, λ = 2$
Distance $PQ = 2 1^{2} + 4^{2} + 5^{2} = 242$

Q. If the image of the point P(1,−2,3) in the plane, 2x+3y−4z+22=0 measured parallel to the line, 1x​=4y​=5z​ is Q, then PQ is equal to :

242​

42​

65​

35​