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 $P(x, y, z)$.According to the given condition,the distance from $P$ to $A(3, 4, -2)$ is equal to the distance from $P$ to

Vedclass · Accepted Answer

$A$ plane whose normal makes equal angles with the axes

Vedclass · Answer

(B) Let the moving point be $P(x, y, z)$.According to the given condition,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 $\vec{n} = (2, 2, 2)$.The direction cosines of the normal are proportional to $(1, 1, 1)$,which means the normal makes equal angles with the coordinate axes.

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

Similar Questions

The equation of a plane containing the point $(1, -1, 1)$ and parallel to the plane $2x + 3y - 4z = 17$ is

The equation of a plane containing the point $(1, -1, 1)$ and parallel to the plane $2x + 3y - 4z = 17$ is

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

$A$ plane meets the coordinate axes at $A, B, C$ and $(\alpha, \beta, \gamma)$ is the centroid of the triangle $ABC$. Then the equation of the plane is

The distance of the point $(1,3,-7)$ from the plane passing through the point $(1,-1,-1)$ having normal perpendicular to both the lines $\frac{x-1}{1}=\frac{y+2}{-2}=\frac{z-4}{3}$ and $\frac{x-2}{2}=\frac{y+1}{-1}=\frac{z+7}{-1}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module