Introduction to...

The points $$A(1, 2, -1), B(2, 5, -2), C(4, 4, -3)$$ and $$D(3, 1, -2)$$ are

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

The chord of contact of tangents from a point $$P$$ to a circle passes  through $$q$$. If $$l_1$$ and $$l_2$$ are the lengths of the tangents from $$P$$ and $$Q$$ to the circle, then $$PQ$$ is equal to

Find the coordinates of the point on the $$x$$-axis that is equidistant from $$P(4,3,1)$$ and $$Q(-2,-6,-2)$$.

If $$(1,-1,0),(-2,1,8)$$ and $$(-1,2,7)$$ are three consecutive vertices of a parallelogram then the fourth vertex is

If $$P(x,y,z)$$ is a point on the line segment joining $$Q(2,2,4)$$ and $$R(3,5,6)$$ such that the projection of $$\overrightarrow { OP } $$ on the axes are $$\displaystyle \frac { 13 }{ 5 } ,\frac { 19 }{ 5 } ,\frac { 26 }{ 5 } $$ respectively, then $$P$$ divides $$QR$$ in ratio

The distance of the point $$\left( 1,-2,3 \right) $$ from the plane $$x-y+z=5$$ measured parallel to the line $$\displaystyle \frac { x }{ 2 } =\frac { y }{ 3 } =\frac { z-1 }{ -6 } $$ is

The ratio in which the plane $$\displaystyle \bar {r} .(\bar {i} - 2 \bar {j} + 3 \bar {k}) = 17$$ divides the line joining the points $$\displaystyle -2 \bar {i} + 4 \bar {j} + 7 \bar {k} $$ and $$\displaystyle 3 \bar {i} - 5 \bar {j} + 8 \bar {k}$$ is

If two vertices of a triangle $$ABC$$ are $$A(-1,2,4)$$and $$B(2,-3,0)$$,and the centroid is $$(2,0,2)$$ then the vertex $$C$$ has the coordinates

Three vertices of a tetrahedron are $$(0,0,0),(6,-5,-1)$$and $$(-4,1,3)$$. If the centroid of the tetrahedron be$$(1,-2,5)$$ then the fourth vertex is