Analytical Geometry 3D

Distance between the point P(2,5,3) from the origin is

• (2,5,3)

• (0,0,0)

• (4,25,9)

• (4,5,9)

If cos $\alpha$  ,cos $\beta$  ,cos $\gamma$  are the direction cosines of a straight line then which one of the following is true?

•  $\cos^2\alpha+\cos^2\beta+\cos^2\gamma=0$  

•  $\sin^2\alpha+\sin^2\beta+\sin^2\gamma=2$  

•  $\cos\alpha+\cos\beta+\cos\gamma=1$  

•  $\sin^2\alpha+\sin^2\beta+\sin^2\gamma=1$  

Determine the direction ratios of the normal to the plane 2x-3y+6z+7=0.

• -2/7,3/7,-6/7

• -2,3,-6

• 2/7,-3/7,6/7

• 2,-3,6

The points (2,1,1) and (2,5,-1) lie on same sides of the plane x-2y+3z+4=0. Say true or false.

• True

• False

The angle between the planes 2x-y+z=6 and x+y+2z=7 is

• $\frac{\pi}{6}$

• $\frac{\pi}{4}$

• $\frac{\pi}{3}$

• $\frac{\pi}{2}$

Two straight lines in space which are not coplanar are called

• Intersecting lines

• perpendicular lines

• parallel lines

• skew lines

The three planes ax+hy+gz=0, hx+by+fz=0, gx+fy+cz=0 pass through a line if

• $a^2+b^2+c^2-2fgh=0$

• $abc+2fgh-af^2-bg^2-ch^2=0$

• $f^2+g^2+h^2-2abc=0$

• $fgh+2abc-fa^2-gb^2-hc^2=0$

Determine the nature of a three planes x+y+2z-2=0, 2x-y+z-1=0 and x+2y-z-3=0.

• Do not intersect at a single point

• Three planes forms a prism

• Intersect at a point

• Three planes have a line of intersection

If the four vertices (3,3,0), (0,-1,0), (2,1,-1), (1,1,1) of a tetrahedron are coplanar then the volume of the tetrahedron is

• 2 cubic units

• 0 cubic units

• 3 cubic units

• 6 cubic units

The two spheres  $x^2+y^2+z^2+6y+2z+8=0\$  and  $x^2+y^2+z^2+6x+8y+4z+20=0\$  intersect 0rthogonally.

• True

• False