`bara.barb=3sqrt2&abs(barb)^2=6` such that `bara=hati+alphahatj+betahatk`. If angle between `bara&barb` is `pi/4` then value of `(alpha^2+beta^2)abs(baratimesbarb)^2` is_____________

If bara,barb,barc are unit vectors such that bara.barb=0,bara.barc and the angle between barb and barc is pi/3 then the value of |bara times barb-bara times barc| is _______

IF |bara|=4,|barb|=2 and the angle between bara and barb is pi/6 then (bara times barb)^2=

If abs(bara)=4,abs(barb)=2 and the angle between bara and barb is (pi)/6 , then abs(bara xx barb)^(2) is equal to

If bara and barb are unit vectors, then the max imum value of abs( bara + barb) + abs(bara - barb) is

Let bara and barb be two unit vectors, and alpha be the angle between them. Then bara + barb is a unit vector, if alpha=

If bara=hati+hatj+hatk , bara.barb=2 and bara times barb=2hati+hatj-3hatk then

If bara=hati+hatj+hatk, bara.barb=2 and bara times barb=2hati+hatj-3hatk then barb is equal to

Let barA= hati + 2hatj + 3hatk and vec B = 3hati + 4hatj + 5hatk The value of the scalar sqrt(|bar A times barB|^2+(barA.barB)^2) is equal to

Given that the vectors bara,barb and barc (no two of them are collinera). Further if (bara +barb) is collinear with barc,(barb+barc) is collinear with bara and |bara|=|barb|=|barc|=sqrt2 . Then the value of |bara.barb+barb.barc+barc.bara| is________