The position vectors of the vertices P, Q and R of `Delta`PQR are `-hat i` + `hat j` + 4`hat k`, 3`hat i`+6 `hat j` + 8 `hat k` and 4`hat i` + `hat j` + `hat k` respectively.
Which of the following is the vector that represents the mediam `vec (PS)`?

The position vectors of the points A,B,C are 2hat i+hat j-hat k,3hat i-2hat j+hat k and hat i+4hat j-hat k respectively.These pooints Form an isosceles triangle Form a right triangle Are collinear Form a scalene triangle

Vectors vec A=hat i+hat j-2hat k and vec B=3hat i+3hat j-6hat k are

The angle between the vectors (hat i + hat j + hat k) and ( hat i - hat j -hat k) is

Show that the point A , B and C with position vectors vec a =3 hat i - 4 hat j -4 hat k = 2 hat i j + hat k and vec c = hat i - 3 hat j - 5 hat k , respectively from the vertices of a right angled triangle.

Show that the four points A,B,C and D with position vectors 4hat i+5hat j+hat k,-(hat j+hat k),3hat j+9hat j+4hat k and 4(-hat i+hat j+hat k) respectively are coplanar.

The position vectors of the points P and Q are 5 hat i+7 hat j- 2 hat k and -3 hat i+3 hat j+6 hat k respecively. The vector vec A=3 hat i-hat j+hat k passes through the point P and the vector vec B=-3 hat i+2 hat j+4 hat k passes through the point Q. A third vector 2 hat i+7 hat j- 5hat k intersects vectors vec A and vec B . Find the position vectors of the points of intersection

If the position vectors of the vertices of a triangle be 2hat(i)+4hat(j)-hat(k), 4hat(i)+5hat(j)+hat(k) and 3hat(i)+6hat(j)-3hat(k) , then the triangle is

Show that the points A,B and C with position vectors,vec a=3hat i-4hat j-4hat kvec b=2hat i-hat j+hat k and vec c=hat i-3hat j-5hat k respectively form the vertices of a right angled triangle.

The unit vector perpendicular to vec A = 2 hat i + 3 hat j + hat k and vec B = hat i - hat j + hat k is

The position vectors of the points Pa n dQ with respect to the origin O are vec a= hat i+3 hat j-2 hat k and vec b=3 hat i- hat j-2 hat k , respectively. If M is a point on P Q , such that O M is the bisector of angleP O Q , then vec O M is a. 2( hat i- hat j+ hat k) b. 2 hat i+ hat j-2 hat k c. 2(- hat i+ hat j- hat k) d. 2( hat i+ hat j+ hat k)