Three Dimension...

Equation of the line which passes through the point with position vector $$(2, 1, 0)$$ and perpendicular to the plane containing the vectors $$i + j$$ and $$j + k$$ is

The projections of a directed line segment on the coordinate axes $$12, 4, 3$$. The direction cosines of the line are

Equation of plane passing through the points $$(2, 2, 1)$$, $$(9, 3, 6)$$ and perpendicular to the plane $$2x+ 6y + 6z-1= 0$$ is

The equation of altitude through $$B$$ to side $$AC$$ is

Given $$A(1,-1,0)$$; $$B(3,1,2)$$;$$C(2,-2,4)$$ and $$D(-1,1,-1)$$ which of the following points neither lie on $$AB$$ nor on $$CD$$

The vector equation of the line $$\displaystyle \frac { x-2 }{ 2 } =\frac { 2y-5 }{ -3 } ,z=-1$$ is $$\displaystyle \overrightarrow { r } =\left( 2\hat { i } +\frac { 5 }{ 2 } \hat { j } -\hat { k }  \right) +\lambda \left( 2\hat { i } -\frac { 3 }{ 2 } \hat { j } +x\hat { k }  \right) $$, where $$x$$ is equal to

If the points $$(0, 1, -2), (3$$, $$\lambda$$,$$ 1)$$ and ($$\mu$$, $$7, 4$$) are collinear, the point on the same line is

A line makes angles $$\alpha$$, $$\beta $$, $$\gamma $$ with the positive directions of the axes of reference. The value of $$\cos 2\alpha +\cos 2\beta +\cos
2\gamma$$ is

The direction cosines of the line joining the points $$(2,3,-1)$$ and $$(3,-2,1) $$ are

Given $$A(1,-1,0)$$; $$B(3,1,2)$$; $$C(2,-2,4)$$ and $$D(-1,1,-1)$$ which of the following points neither lie on $$AB$$ nor on $$CD$$?