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

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

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

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

If p_(1) and p_(2) are the lengths of perpendiculars from the points hati - hatj + 3hatk and 3hati + 4hatj + 3hatk to the plane barr *(5hati + 2hatj - 7hatk) + 8 = 0 , then

The value of lambda, for which the four points 2hati+3hatj-hatk, hati-2hatj+3hatk, 3hati+4hatj-2hatk, hati-6hatj+lambda hatk are coplanar, is

The ratio in which the plane vecr.(hati-2hatj+3hatk)=17 divides the line joining points -2hati+4hatj+7hatk and 3hati-5hatj+8hatk is

The value of lamda for which the four points 2hati+3hatj-hatk,hati+2hatj+3hatk,3hati+4hatj-2hatk and hati-lamdahatj+6hatk are coplanar.

The vector equation of the line passing through a point with position vector 2hati-hatj+hatk and parallel to the line joining the points with position vectors -hati+4hatj+hatk and hati+2hatj+2hatk is r=(2hati-hatj+hatk)+lambda(xhati-2hatj+hatk) where x is equal to