Three Dimension...

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

If O is the origin and A is the point $$(a, b, c)$$, then the equation of the plane through A and at right angles to OA is

The values of $$a$$ for which point $$(8, -7, a), (5, 2, 4)$$ and $$(6, -1, 2)$$ are collinear.

The equation of the perpendicular from the point $$(\alpha, \beta, \gamma)$$ to the plane $$ax + by + cz + d = 0$$ is

The straight line $$\displaystyle \frac{x - 3}{3} = \frac{y - 2}{1} = \frac{z - 1}{0}$$ is

A straight line $$L$$ on the $$xy$$-plane bisects the angle between $$OX$$ and $$OY$$. What are the direction cosines of$$ L$$?

The equation of the plane through $$(1, 2, 3)$$ and parallel to the plane $$2x + 3y - 4z = 0$$ is

If $$M$$ denotes the mid-point of the line segment joining $$ A( 4\widehat{i} + 5\widehat{j}- 10 \widehat{k})$$ and $$ B(-\widehat{i} + 2 \widehat{j} + \widehat{k})$$, then the equation of the plane through $$M$$ and perpendicular to $$AB$$, is

The point collinear with $$(4, 2, 0)$$ and $$(6, 4, 6)$$ among the following is

If the points $$a(1, 2, -1), B(2, 6, 2)$$ and $$c(\lambda, -2, -4)$$ are collinear then $$\lambda$$ is