Three Dimension...

If the image of the point $$\displaystyle \left ( 1, \: 1, \: 1 \right )$$ by a plane $$\displaystyle \left ( 3, \: -1, \: 5 \right )$$ then the equation of the plane is

Which of the triplet can not represent direction cosine of a line

The direction cosines of the normal to the plane $$\displaystyle 5\left ( x - 2 \right ) = 3\left ( y - z \right )$$ are

The position vectors of three points are $$2\vec{a}-\vec{b}+3\vec{c}$$, $$\vec{a}-2\vec{b}+\lambda \vec{c}$$ and $$\mu \vec{a}-5\vec{b}$$ where $$\vec{a}, \vec{b}, \vec{c}$$ are non coplanar vectors, then the points are collinear when

The angle between the straight lines $$\displaystyle \frac { x+1 }{ 2 } =\frac { y-2 }{ 5 } =\frac { z+3 }{ 4 } $$ and $$\displaystyle \frac { x-1 }{ 1 } =\frac { y+2 }{ 2 } =\frac { z-3 }{ -3 } $$ is

Let $$A= \left ( 1,2,2 \right )$$, $$B=\left ( 2,3,6 \right )$$and $$C= \left ( 3,4,12 \right )$$. The direction cosines of a line equally inclined with $$OA,OB$$ and $$OC$$ , where $$O$$ is the origin, are

A st. line which makes angle of $$\displaystyle 60^{\circ}$$ with each of y - and z - axes, is inclined with x - axis at an angle

Find the equations of the plane through the point $$\displaystyle \left ( x_{1},y_{1},z_{1} \right )$$ and perpendicular to the straight line $$\displaystyle \frac{x-\alpha }{l}=\frac{y-\beta }{m}=\frac{z-\gamma }{n}$$

Which of the following triplets give the direction cosines of a line ?

If a line makes angles $$\displaystyle \alpha ,\beta ,\gamma $$ with axes of co-ordinates, then $$\displaystyle \cos 2\alpha +\cos 2\beta +\cos 2\gamma$$ is equla to