The position vector of a point is where and . If , then the number of possible positions of is

Let A vector in the plane of and whose projection on is , is

Let then holds for

The distance of the point from the line parallel to vector and passing through the point is

For such questions, we should know different formulas of distances for line or plane.

The value of 'a' so that the volume of parallel piped formed by and   becomes minimum is

For such questions, we should know the volume of parallelepiped.

There are following extraction process of silver but not

in terms  terms only  is

Two sides of triangle are given by equation  and angle between
the sides is  Then perimeter of the triangle is