Three Dimension...

If the direction cosine of a directed line be $$a, 3a, 7a$$ then $$a =$$

The direction ratios of the line $$6x - 2 = 3y + 1 = 2z - 2$$ are 

If $$l,m,n$$ are d.c's of vector $$\overline {OP}$$ then maximum value of $$lmn$$ is

If O is the origin and the coordinates of P is $$(1, 2, -3)$$, then find the equation of the plane passing through P and perpendicular to OP.

The direction cosines of two lines are related by $$l+m+n=0$$ and $$al^2+bm^2+cn^2=0$$. The lines are parallel if

The direction cosines of a line segment AB are $$ - \dfrac{2}{{\sqrt {17} }},\dfrac{3}{{\sqrt {17} }}, - \dfrac{2}{{\sqrt {17} }}$$. If $$AB=\sqrt {17} $$ and the coordinates of A are $$(3,-6,10)$$, then the coordinates of B are 

The foot of the perpendicular drawn from the origin to a plane is $$(1, 2, -3)$$. Find the equation of the plane.

If a  line has the direction ratios $$4, -12,18$$ then find its direction cosines.

A mirror and a source of light are situated at the origin $${\rm O}$$ and at a point on $${\rm O}X$$, respectively. A ray of light from the source strikes the mirror and is reflected. If the direction ratios of the normal to the plane are $$1,\, - 1,\,1$$, then find the DCs of the reflected ray.

The direction`cosines of a line equally inclined to three mutually perpendicular lines having D.C.'s as $${\ell _1}{m_1}{n_1}:{\ell _2}{m_2}{n_2}:{\ell _3}{m_3}{n_3}\,\,$$ are