Tag: introduction to three dimensional geometry

$P$ and $Q$ are points on the line joining $A(-2,5)$ and $B(3,1)$ such that $AP=PQ=QB$. Then, the distance of the midpoint of $PQ$ from the origin is

A line passes through two point $A (2, -3, -1)$ and $B (8, -1, 2)$. The coordinates of a point on this line at a distance of $14$ units from $A$ are

If  $C _1:{x^2+y^2}-20x+64=0$ and $C _2:{x^2+y^2}+30x+144=0$. Then the length of the shortest line segment $PQ$  which touches $C _1$ at $P$ and  to  $C _2$ at $Q$ is

The distance of the point $(4,7)$ from the $x-$ axis is 

Minimum distance between the curves
$y^{2}=4x$ & $x^{2}+y^{2} -12x+31=0$ is -

The distance of the point $(2,3)$ form the line $x-2y+5=0$ measured in a direction parallel to the line $x-3y=0$ is

The distance of the point $(2,1,-1)$ from the line $\dfrac{x-1}{2}=\dfrac{y+1}{1}=\dfrac{z-3}{-3}$ measured parallel to the plane $x+2y+z=4$ is

The distance of the point (1,3) from the line 2x-3y+9=0 measured along a line x-y+1=0 is

If $L _1$ is the line of intersection of the plane $2x-2y+3z-2=0, x-y+z+1=0$ and $L _2$ is the line of intersection of the plane   $x+2y-z-3=0, 3x-y+2z-1=0$, then the distance of origin from from the plane containing the lines $L _1$ + $L _2$ is :

The equation of plane which is passing through the point $(1,2,3)$ and which is at maximum distance from the point $(-1,0,2)$ is