Three Dimension...

If $$A(p,q,r)$$ and $$B=(p\prime ,q\prime ,r\prime )$$ are two points on the line $$\lambda x=\mu y=yz$$ such that $$OA=3,OB=4$$ then $$pp\prime +qq\prime +rr\prime $$ is equal to 

The angle between the lines whose de's satisfy the equation $$l+m+m=0$$ and $$l^2+m^{2}-n^{2}=0$$ is 

The angle between the lines, whose direction ratios are $$1,1,2$$ and $$\sqrt { 3 } - 1 , - \sqrt { 3 } - 1,4 ,$$ is

The directions cosines of the line which is perpedicular to the lines whose direction cosines are proportional to (1, -1, 2) and (2,-1,-1) are:

If a plane passes through the point $$(1, 1, 1)$$ and is perpendicular to the line $$\dfrac{x-1}{3}=\dfrac{y-1}{0}=\dfrac{z-1}{4}$$ then its perpendicular distance from the origin is 

The direction cosines of a line equally inclined to three mutually perpendicular lines having direction cosines as $$l_{1},m_{1},n_{1};l_{2},m_{2},n_{2}$$ and $$l_{3},m_{3},n_{3}$$ are

$$l=m=n=1$$ represent the direction cosines of the 

If the points (p. 0), (0, q) and (1, 1) are collinear then $$\dfrac { 1 }{ p } +\dfrac { 1 }{ q } $$ is equal to 

The direction ratios of the line
$$x-y+z-5=\quad 0\quad =\quad x-3y-6\quad are$$

The direction cosines of a line equally inclined to three mutually perpendicular lines having direction cosines as $$l_1$$, $$m_1$$, $$n_1$$ : $$l_2$$, $$m_2$$, $$n_2$$ and   $$l_3$$, $$m_3$$, $$n_3$$ are