Vectors & 3D Geometry PYQ

The volume of the parallelepiped formed by vectors a=i+2j-k, b=2i-j+3k, c=3i+j+2k is:

The position vectors of points A and B are 2i+3j+k and 4i+j-2k. The position vector of the midpoint of AB is:

The image of the point (1,2,3) in the plane x+y+z=9 is:

The projection of vector a=2i-3j+6k on vector b=i+2j+2k is:

The scalar triple product [i j k] is:

The equation of the plane passing through (1,2,3) and perpendicular to the vector 2i+3j-k is:

The shortest distance between lines (x-1)/2=(y+1)/3=z/1 and (x+1)/5=(y-2)/1=z/(-1) is:

The direction cosines of the line joining points (1,2,3) and (4,6,3) are:

The angle between vectors a=i+j and b=j+k is:

If vectors a=2i+3j+k and b=i-j+2k then a×b is: