Find the mid point of the ine segment joining the points `P(2hati+3hatj+3hatk) and Q(4hati+hatj-2hatk)`

Find the position vector of the mid-point of the vector joining the points A(3hati + 2hatj + 6hatk) and B(hati + 4hatj - 2hatk)

The length of line segment joining the points 2hati-2hatj+3hatk, 5hati+2hatj+3hatk is

Find the position vector of a point R which divides the line joining the point P(hati + 2hatj - hatk) and Q(-hati + hatj + hatk) in the ratio 2 : 1 , (i) internally and (ii) externally.

The cartesian equation of a line passing through the point having position vector 2hati +hatj - hatk and parallel to the line passing joining the points -hati + hatj + 4hatk and hati + 2hatj + 2hatk , is

Find the position vector of a point R which divides the line joining two points P(hati+2hatj-hatk) and Q(-hati-hatj+hatk) in the ratio 2:1: internally

Find the position vector of a point R which divides the line joining two points P(hati-2hatj-hatk) and Q(-hati-hatj+hatk) in the ratio 2:1: externally

Find the vector equation of the plane passing through the point hati + hatj -2hatk and hati + 2hatj + hatk, 2hati - hatj + hatk.

Find the points of intersection of the line vecr = 2hati - hatj + 2hatk + lambda(3hati + 4hatj + 2hatk) and the plane vecr.(hati - hatj + hatk) = 5

The position vector of the point in which the line joining the points hati-2hatj+hatk and 3hatk-2hatj cuts the plane through the origin and the points 4hatj and 2hati+hatk is

Find the distance of the point (hati+2hatj-3hatk) from the plane vecr.(2hati-5hatj-hatk)=4 .