If the three consectutive vertices of a parallelogram are `bar(i)+bar(j)+bar(k),3bar(j)+5bar(k)` and `7bar(i)+9bar(j)+11bar(k)` then fourth vertex is

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

The adjacent sides of a parallelogram are 2bar(i)+4bar(j)-5bar(k) and bar(i)+2bar(j)+3bar(k) then the unit vector parallel to a diagonal is

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=

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

The position vectors of the vertices of a triangle are 3bar(i)+4bar(j)+5bar(k),bar(i)+7bar(k) and 5bar(i)+5bar(j) The distance between the circumcentre and orthocentre is

The P.V's of the vertices of a triangle are 2bar(i)+3bar(j)+4bar(k),4bar(i)+6bar(j)+3bar(k),3vec i+2bar(j)+3bar(k) P.V.of orthocenter is

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=

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 volume of parallelo piped whose coterminus edges are bar(i)-bar(j),2bar(i)+bar(j)+bar(k),bar(i)-bar(j)+3bar(k) is

If the P.V.'s of A,B,C are 3bar(i)+4bar(j)+6bar(k),4bar(i)-6bar(j)+3bar(k) and -6bar(i)+3bar(j)+4bar(k) then the incentre of Delta ABC is