The two vectors `hatj+hatk` and `3hati-hatj+4hatk` represent the two sides AB and AC respectively of a `/_\ABC`. Find the lengthof the median through A

If vectors vec(AB) = -3hati+ 4hatk and vec(AC) = 5hati -2hatj+4hatk are the sides of a Delta ABC , then the length of the median throught A is

If the vectors vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj-4hatk are the sides of a triangle ABC, then the length of the median through A is :

The position vectors of two points A and B are 3 hati+hatj+2hatk and hati-2hatj-4hatk respectively. Find the equation of the plane passing through B and perpendicular to vec(AB)

The position vectors of A and B are 2hati-9hatj-4hatk and 6hati-3hatj+8hatk respectively, then the magnitude of AB is

Show that the vectors 2hati-3hatj+4hatk and -4hati+6hatj-8hatk are collinear.

If hati+hatj+hatk, 2hati+5hatj, 3hati+2hatj-3hatk and hati-6hatj-hatk are the position vectors of points A, B, C and D respectively, then find the angle between AB and CD. Deduce that AB and CD are collinear.

If A and B are two points whose position vectors are 3hati+2hatj-2hatk and hati-3hatj-hatk respectively. Find the position vectors of the points dividing the segment AB internally in the ratio 1:3.

If A and B are two points whose position vectors are 3hati+2hatj-2hatk and hati-3hatj-hatk respectively. Find the position vectors of the points dividing the segment AB externally in the ratio 3:1.

Dot products of a vector with vertices hati+hatj-3hatk,hati+3hatj-2hatk and 2hati+hatj+4hatk are 0,5 and 8 respectively. Find the vector.