The length of the perpendicular from the orig | vedclass

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

Question

(A) The vector equation of the plane passing through three non-collinear points with position vectors $a, b, c$ is given by $r \cdot (a 	imes b + b \

Vedclass · Accepted Answer

$\frac{[a, b, c]}{|a 	imes b + b 	imes c + c 	imes a|}$

Vedclass · Answer

(A) The vector equation of the plane passing through three non-collinear points with position vectors $a, b, c$ is given by $r \cdot (a 	imes b + b 	imes c + c 	imes a) = [a, b, c]$.This equation is in the form $r \cdot n = p$,where $n = a 	imes b + b 	imes c + c 	imes a$ is the normal vector to the plane and $p = [a, b, c]$.The length of the perpendicular from the origin to the plane $r \cdot n = d$ is given by $\frac{|d|}{|n|}$.Substituting the values,the length of the perpendicular is $\frac{|[a, b, c]|}{|a 	imes b + b 	imes c + c 	imes a|}$.Since the scalar triple product $[a, b, c]$ represents the volume of the parallelepiped formed by vectors $a, b, c$,and the denominator represents the magnitude of the normal vector,the correct expression is $\frac{[a, b, c]}{|a 	imes b + b 	imes c + c 	imes a|}$.

Point	Plane
$(-6, 0, 0)$	$2x - 3y + 6z - 2 = 0$

The length of the perpendicular from the origin to the plane passing through three non-collinear points $a, b, c$ is

Similar Questions

$A$ variable plane at a constant distance $p$ from the origin meets the coordinate axes at $A, B, C$. Through these points,planes are drawn parallel to the coordinate planes. The locus of the point of intersection is

In the following case,find the distance of the given point from the corresponding given plane.

Point Plane

$(-6, 0, 0)$ $2x - 3y + 6z - 2 = 0$

The equation of a plane passing through $(-1, 2, 3)$ and whose normal makes equal angles with the coordinate axes is

$A$ plane passes through the point $(3, 5, 7)$. If the direction ratios of its normal are equal to the intercepts made by the plane $x+3y+2z=9$ with the coordinate axes,then the equation of that plane is

If $(3,4,-7)$ is the foot of the perpendicular drawn from the point $(-2,3,6)$ to the plane $\pi$,then the sum of the intercepts made by the plane $\pi$ on the $X$ and $Y$-axes is

Vedclass Test Series

Exam Paper Generator

Online Exam Module