`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

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

Consider the parallelopiped with sides bar(a)=3bar(i)+2bar(j)+bar(k),bar(b)=bar(i)+bar(j)+2bar(k) and bar(c)=bar(i)+3bar(j)+3bar(k) then angle between bar(a) and the plane containing the face determined by bar(b) and bar(c) 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=

Given bar(a)=bar(i)+2bar(j)+3bar(k),bar(b)=2bar(i)+3bar(j)+bar(k),bar(c)=8bar(i)+13bar(j)+9bar(k) , the linear relation among them if possible is

If bar(a)=bar(i)+2bar(j)+bar(k) , (b)=bar(i)-bar(j)+bar(k) and bar(c)=bar(i)+bar(j)-bar(k) . A vector in the plane of bar(a) and bar(b) whose projection on bar(c) is (1)/(sqrt(3)) is

Let bar(a)=bar(i)+2bar(j)+4bar(k),bar(b)=bar(i)+lambdabar(j)+4bar(k) and bar(c)=2bar(i)+4bar(j)+(lambda^(2)-1)bar(k) be coplanar vectors. Then the nonzero vector bar(a)timesbar(c) is

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 lambda=(the projection of bar(a) on bar(b))/( the projection of bar(b) on bar(a)) then the value of lambda is

The value of a for which the angle between bar(a)=2a^(2)bar(i)+4abar(j)+bar(k) and bar(b)=7bar(i)-2bar(j)+abar(k) is obtuse and the angle between bar(b) and z-axis is acute and less than (pi)/(6) is