A point moves such that its distances from th | vedclass

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

Question

(B) Let the moving point be $P(x, y, z)$.Given that the distance from $P$ to $A(3, 4, -2)$ is equal to the distance from $P$ to $B(2, 3, -3)$.So,$PA^2

Vedclass · Accepted Answer

$A$ plane whose normal is equally inclined to axes

Vedclass · Answer

(B) Let the moving point be $P(x, y, z)$.Given that the distance from $P$ to $A(3, 4, -2)$ is equal to the distance from $P$ to $B(2, 3, -3)$.So,$PA^2 = PB^2$.$(x - 3)^2 + (y - 4)^2 + (z + 2)^2 = (x - 2)^2 + (y - 3)^2 + (z + 3)^2$Expanding both sides:$(x^2 - 6x + 9) + (y^2 - 8y + 16) + (z^2 + 4z + 4) = (x^2 - 4x + 4) + (y^2 - 6y + 9) + (z^2 + 6z + 9)$Canceling $x^2, y^2, z^2$ from both sides:$-6x - 8y + 4z + 29 = -4x - 6y + 6z + 22$Rearranging the terms:$2x + 2y + 2z = 7$This is the equation of a plane. The normal vector to this plane is $\vec{n} = 2\hat{i} + 2\hat{j} + 2\hat{k}$.Since the components of the normal vector are equal,the normal is equally inclined to the coordinate axes.

$A$ point moves such that its distances from the points $(3, 4, -2)$ and $(2, 3, -3)$ remain equal. The locus of the point is

Similar Questions

$A$ plane passes through $(2,3,-1)$ and is perpendicular to the line having direction ratios $3,-4,7$. The perpendicular distance from the origin to this plane is

$A$ plane is parallel to two lines,whose direction ratios are $1, 0, -1$ and $-1, 1, 0$ and it contains the point $(1, 1, 1)$. If it cuts coordinate axes ($X, Y, Z$-axes respectively) at $A, B, C$,then the volume of the tetrahedron $OABC$ is (in cubic units):

The distance of the plane $2x - y - 2z - 9 = 0$ from the origin is $d$ units.

If a plane meets the coordinate axes at $A, B$ and $C$ in such a way that the centroid of $\triangle ABC$ is at the point $(1, 2, 3)$,then the equation of the plane is

The foot of the perpendicular drawn from the origin to the plane is $(4, -2, -5)$. Hence,the equation of the plane is

Vedclass Test Series

Exam Paper Generator

Online Exam Module