3D Geometry: Let the image of the point P(2,-1,3) in the plane x+2y-z=0 be Q .… | JEE Main 2023 | Yukti Vault

Yukti Vault

JEE Main 2023 (Online) 1st February Morning ShiftQuestion 1

Let the image of the point $P(2,-1,3)$ in the plane $x+2y-z=0$ be $Q$. Then the distance of the plane $3x+2y+z+29=0$ from the point $Q$ is

3D Geometry

$\frac{22\sqrt2}{7}$$\frac{24\sqrt2}{7}$$2\sqrt{14}$$3\sqrt{14}$✓ Correct answer

Solution

$Q=P-2\frac{(2-2-3)}{6}(1,2,-1)=(3,1,2)$. Distance from $3x+2y+z+29=0$: $\frac{|9+2+2+29|}{\sqrt{14}}=3\sqrt{14}$.

More from 3D Geometry

Let the position vectors of the vertices A , B and C of a tetrahedron ABCD be hati+2hatj+hatk ,…
If the square of the shortest distance between the lines (x-2)/(1)=(y-1)/(2)=(z+3)/(-3) and…
The length of the perpendicular from the point (1,-2,5) on the line passing through (1,2,4) and parallel to…
The distance of the point (7,-3,-4) from the plane containing the points (2,-3,1) , (-1,1,-2) and (3,-4,2)…
If the shortest distance between the lines (x-1)/(2)=(y-2)/(3)=(z-3)/(lambda) and…
A plane passing through the point (3,1,1) contains two lines whose direction ratios are 1,-2,2 and 2,3,-1…
Let (x-2)/(3)=(y+1)/(-2)=(z+3)/(-1) lie on the plane px-qy+z=5 , for some p,qinmathbfR . The shortest…
The square of the distance of the point of intersection of the line (x-1)/(2)=(y-2)/(3)=(z+1)/(6) and the…