The position vectors of points A,B,C and D are `A=3hati+4hatj+5hatk`,`B=4hati+5hatj+6hatk`,`C=7hati+9hatj+3hatk`, and `D=4hati+6hatj`, then the displacement vectors AB and CD are

The position vectors of points A,B,C and D are A=3hati+4hatj+5hatk , B=4hai+5hatj+6hatk , C=7hati+9hatj+3hatk , and D=4hati+6hatj , then the displacement vectors AB and CD are

The position vectors of the points A, B, C and D are 4hati+3hatj-hatk , 5hati+2hatj+2hatk , 2hati-2hatj-3hatk and 4hati-4hatj+3hatk respectively. Show that AB and CD are parallel.

If the position vectors of the points A, B, C, D are hati+hatj+hatk, 2hati+5hatj, 3hati +2hatj-3hatk and hati-6hatj-hatk respectively, then the angle between the vectors vec(AB) and vec(CD) is -

The position vectors of the point A, B, C and D are 3hati-2hatj -hatk, 2hati+3hatj-4hatk, -hati+hatj+2hatk and 4hati+5hatj +lamda hatk , respectively. If the points A, B, C and D lie on a plane, find the value of lamda .

The position vectors of the point A, B, C and D are 3hati-2hatj -hatk, 2hati+3hatj-4hatk, -hati+hatj+2hatk and 4hati+5hatj +lamda hatk , respectively. If the points A, B, C and D lie on a plane, find the value of lamda .

The position vectors of the points A,B and C are (2hati + hatj - hatk), (3hati - 2hatj + hatk) and (hati + 4hatj - 3hatk) respectively. Show that the points A,B and C are collinear.

If the position vectors of A, B, C, D are 3hat i +2 hat j+hatk, 4 hati +5hatj+5hatk, 4hati +2hatj -2hatk, 6hati +5hatj-hatk respec-tively then the position vector of the point of intersection of lines AB and CD is

Position vectors of four points A,B,C,D are 4hati +5hatj+hatk,-(hatj+hatk),3hati+9hatj+4hatk and 4(-hati+hatj+hatk) respectively . Prove that they are coplanar.

The position vectors of the points A,B,C and D are 6 hati - 7 hatj , 16 hati - 29 hatj - 4 hatk , 3 hati - 6 hatk and 2 hati + 5 hatj + 10 hatk respectively. Show that the points A,B,C and D are non coplanar.