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

undersetbar(a)bar(a)=2bar(i)+bar(j)+3bar(k),bar(b)=pbar(i)+bar(j)+qbar(k) and bar(b)xxbar(a)=bar(0)

undersetbar(a)bar(a)=2bar(i)+bar(j)+3bar(k),bar(b)=pbar(i)+bar(j)+qbar(k) and bar(b)xxbar(a)=bar(0)

bar(b)=bar(i)-2bar(j)-3bar(k),bar(b)=2bar(i)+bar(j)-bar(k),bar(c)=bar(i)+ 3bar(j)-2bar(k) then bar(a).(bar(b)xxbar(c))

If bar(a)=2bar(i)-bar(j)-bar(k),bar(b)=bar(i)+2bar(j)-3bar(k) and bar(c)=3mp mubar(j)+5bar(k) are coplanar then mu root of the equation

bar(a)=2bar(i)+3bar(j)-4bar(k),bar(b)=bar(i)+bar(j)+bar(k),bar(c)=4bar(i)+2bar(j)+3bar(k) then |bar(a)xx(bar(b)xxbar(c))|=

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

The lines bar(r)=bar(i)+bar(j)-bar(k)+s(3bar(i)-bar(j)) and bar(r)=4bar(i)-bar(k)+t(2bar(i)+3bar(k))

If bar(a)=2bar(i)-3bar(j)+5bar(k),bar(b)=-bar(i)+4bar(j)+2bar(k) then find bar(a)timesbar(b) and unit vector perpendicular to both bar(a) and bar(b) .

The reciprocal of bar(a) where bar(a)=-bar(i)+bar(j)+bar(k),bar(b)=bar(i)-bar(j)+bar(k),bar(c)=bar(i)+bar(j)+bar(k) 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