If `2bar(i)+3bar(j)-6bar(k)`, `6bar(i)-2bar(j)+3bar(k)` are two consecutive sides of a triangle, then perimeter of triangle is

The vectors bar(AB)=3bar(i)+4bar(k) and bar(AC)=5bar(i)-2bar(j)+4bar(k) are the sides of a triangle ABC .The length of the median through A

bar(OA)=6bar(i)+3bar(j)-4bar(k),bar(OB)=2bar(j)+bar(k),bar(OC)=5bar(i)-bar(j)+2bar(k) are coterminous edges of a parallelepiped,then the height of the parallelepiped drawn from the vertex A is

If bar(a)=2bar(i)-3bar(j)+6bar(k) , bar(b)=-2bar(i)+2bar(j)-bar(k) and k =(the projection of bar(a) on bar(b)) /(the projection of bar(b) on bar(a)) then the value of 3k=

If bar(a)=bar(i)-2bar(j)-bar(k) , bar(b)=-2bar(j)+bar(k) are two vectors and bar(c) is a vector such that bar(c)=bar(a) times bar(b) then |bar(a)|:|bar(b)|:|bar(c)| =

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

If bar(a)=2bar(i)-3bar(j)+6bar(k), bar(b)=-2bar(i)+2bar(j)-bar(k) and lambda=(the projection of bar(a) on bar(b))/( the projection of bar(b) on bar(a)) then the value of lambda is

If bar(a)=bar(i)+2bar(j)+bar(k),bar(b)=2bar(j)+bar(k)-bar(i), then component of bar(a) perpendicular to bar(b) is

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

bar(F),=abar(i)+3bar(j)+6bar(k) and , bar(r),=2bar(i)-6bar(j)-12bar(k) .The value of a for which the toque is 0

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