The vector area of the triangle formed by the points `bar(i)+2bar(j)+3bar(k),2bar(i)+3bar(j)+bar(k)` and `3bar(i)+bar(j)+2bar(k)` is

The vectors bar(i)+4bar(j)+6bar(k),2bar(i)+4bar(j)+3bar(k) and bar(i)+2bar(j)+3bar(k) form

If the volume of tetrahedron with edges bar(i)+bar(j)-bar(k) , bar(i)+abar(j)+bar(k) and bar(i)+2bar(j)-bar(k) is (a)/(6) then a=

A point on the line bar(r)=(1-t)(2bar(i)+3bar(j)+4bar(k))+t(3bar(i)-2bar(j)+2bar(k))

If the position vectors of A,B and C are respectively 2bar(i)-bar(j)+bar(k),bar(i)+3bar(j)-5bar(k) and 3bar(i)-4bar(j)-4bar(k) then cos^(2)A=

If the volume of a parallelopiped with coterminous edges 4bar(i)+5bar(j)+bar(k) , -bar(j)+bar(k) and 3bar(i)+9bar(j)+pbar(k) is 34 cubic units, then p=

In a triangle ABC ,right angled at the vertex A ,if the position vectors of A, B and C are respectively 3bar(i)+bar(j)-bar(k), -bar(i)+3bar(j)+pbar(k) and 5bar(i)+qbar(j)-4bar(k), then the points (p,q) lies on a line

If the volume of a parallelopiped with coterminous edges 4bar(i)+5bar(j)+bar(k),-bar(j)+bar(k) and 3bar(i)+9bar(j)+pbar(k) is 34 cubic units, then p=

The angle between the planes bar(r)*(2bar(i)-3bar(j)+4bar(k))+11=0 and bar(r).(3bar(i)-2bar(j)-3bar(k))+27=0 is

The angle between the planes bar(r)*(2bar(i)-3bar(j)+4bar(k))+11=0 and "bar(r)*(3bar(i)-2bar(j))=0. is

The angle between planes bar(r).(2bar(i)-3bar(j)+4bar(k))+11=0 and bar(r).(3bar(i)-2bar(j)-3bar(k))+27=0 is