The position vectors of the four angular points of a tetrahedron are `A( hat j+2 hat k),B(3 hat i+ hat k), C(4 hat i+3 hat j+6 hat k)a n dD(2 hat i+3 hat j+2 hat k)dot` Find the volume of the tetrahedron `A B C Ddot`

Show that the points A(-2 hat i+3 hat j+5 hat k), B( hat i+2 hat j+3 hat k) and C(7 hat i-3 hat k) are collinear.

underset with a = 2hat i + hat j-3hat k, vec b = -hat i + hat j + 2hat k, vec c = 4hat i + 3hat k

Find the area of the rriangle formed by the tips of the vectors, vec a= (2 hat I - hat j+ 3 hat k), vec b= 4 hat I + 3 hat j-hat k , vec C= 3 hat I - hat j + 2 hat k .

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

Show that the points A(-2hat i+3hat j+5hat k),B(hat i+2hat j+3hat k) and C(7hat i-hat k) are collinear.

If vec a= hat i+ hat j+ hat k , vec b=2 hat i- hat j+3 hat k a n d vec c= hat i-2 hat j+ hat k find a unit vector parallel to 2 vec a- vec b+3 vec cdot

If the vertices of a tetrahedron have the position vectors vec 0,hat i+hat j,2hat j-hat k and hat i+hat k then the volume of the tetrahedrom is

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

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