If position vectors of points P,Q,R are `bar(i)+4bar(j)-2bar(k),2bar(i)+bar(j)-2bar(k),quad -5bar(j)+bar(k)` respectively then the distance from P to QR 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 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

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

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

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

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 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=

If the volume of the tetrahedron with edges 2bar(i)+bar(j)+bar(k),bar(i)+abar(j)+bar(k) and vec i+2bar(j)-bar(k) is one cubic unit then a=

If the vectors bar(a)=-2bar(i)+3bar(j)+ybar(k) and bar(b)=xbar(i)-6bar(j)+2bar(k) are collinear, then the value of x+y is