Let Q be the foot of the perpendicular drawn | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The equation of the plane is $x + 2y + z = 14$.The length of the perpendicular $PQ$ from point $P(1, 2, 3)$ to the plane is given by:$PQ = \left|

Vedclass · Accepted Answer

$\sqrt{3}$

Vedclass · Answer

(B) The equation of the plane is $x + 2y + z = 14$.The length of the perpendicular $PQ$ from point $P(1, 2, 3)$ to the plane is given by:$PQ = \left| \frac{1(1) + 2(2) + 1(3) - 14}{\sqrt{1^2 + 2^2 + 1^2}} ight| = \left| \frac{1 + 4 + 3 - 14}{\sqrt{6}} ight| = \left| \frac{-6}{\sqrt{6}} ight| = \sqrt{6}$.In the right-angled triangle $	riangle PQR$,where $\angle PQR = 90^{\circ}$ and $\angle PRQ = 60^{\circ}$,we have:$QR = PQ \cot(60^{\circ}) = \sqrt{6} 	imes \frac{1}{\sqrt{3}} = \sqrt{2}$.The area of $	riangle PQR$ is given by:Area $= \frac{1}{2} 	imes PQ 	imes QR = \frac{1}{2} 	imes \sqrt{6} 	imes \sqrt{2} = \frac{1}{2} 	imes \sqrt{12} = \frac{1}{2} 	imes 2\sqrt{3} = \sqrt{3}$.

Let $Q$ be the foot of the perpendicular drawn from the point $P(1, 2, 3)$ to the plane $x + 2y + z = 14$. If $R$ is a point on the plane such that $\angle PRQ = 60^{\circ}$,then the area of $\triangle PQR$ is equal to:

Similar Questions

The line passing through the points $(1, 1, -1)$ and $(3, -1, 0)$ makes an angle of $\operatorname{Tan}^{-1}\left(\frac{1}{\sqrt{8}}\right)$ with the plane $\sqrt{\lambda} x + 3y + 6z = 17$. Then $\lambda =$

The length of the projection of the line segment joining the points $(5, -1, 4)$ and $(4, -1, 3)$ on the plane $x + y + z = 7$ is:

The point $P$ is the intersection of the straight line joining the points $Q(2, 3, 5)$ and $R(1, -1, 4)$ with the plane $5x - 4y - z = 1$. If $S$ is the foot of the perpendicular drawn from the point $T(2, 1, 4)$ to $QR$,then the length of the line segment $PS$ is

The Cartesian equation of a line passing through $(1, 2, 3)$ and parallel to the planes $x - y + 2z = 5$ and $3x + y + z = 6$ is:

The length (in units) of the projection of the line segment,joining the points $(5,-1,4)$ and $(4,-1,3)$,on the plane $x+y+z=7$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module