Straight LineHard
Question
Let $Q(a,b,c)$ be the image of the point $P(3,2,1)$ in the line $\frac{x - 1}{1} = \frac{y}{2} = \frac{z - 1}{1}$. Then the distance of Q from the line $\frac{x - 9}{3} = \frac{y - 9}{2} = \frac{z - 5}{- 2}$ is
Options
A.6
B.8
C.7
D.5
Solution
drs of $PN = < r - 2,2r - 2,r >$
$${1.(r - 2) + 2(2r - 2) + 1.(r) = 0 }{6r = 6 \Rightarrow r = 1 }{\therefore N \equiv (2,2,2) }{\Rightarrow Q \equiv (1,2,3) }$$
$${AQ = \sqrt{64 + 49 + 4} = \sqrt{117} }{AM = \left| \frac{24 + 14 - 4}{\sqrt{9 + 4 + 4}} \right| = \frac{34}{\sqrt{17}} = 2\sqrt{17} }{\therefore QM = \sqrt{117 - 68} = \sqrt{49} = 7}$$
Create a free account to view solution
View Solution FreeMore Straight Line Questions
The lines x + (a − 1) y + 1 = 0 and 2x + a2y − 1 = 0 are perpendicular if...The equations of the lines on which the perpendiculars from the origin make 30o angle with x-axis and which form a trian...Let the direction cosines of two lines satisfy the equations: $4\mathcal{l} + m - n = 0$ and $2mn + 10n\mathcal{l} + 3\m...For a > b > c > 0, the distance between (1, 1) and the point of intersection of the lines ax + by + c = 0 and bx + ay + ...A lizard, at an initial distance of 21 cm behind an insect, moves from rest with an acceleration of 2 cm/s2 and pursues ...