If `3bar(i)+3bar(j)+sqrt(3)bar(k),bar(i)+bar(j),sqrt(3)bar(i)+sqrt(3)bar(j)+lambdabar(k)` are coplanar vectors then `lambda=`

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

If three vectors bar(a)=bar(i)+bar(j)+bar(k),bar(b)=bar(i)-2a^(2)bar(j)+abar(k),bar(c)=bar(i)+(a+1)bar(j)-abar(k) are linearly dependent vectors then the real a lies in the interval.

If there vectors bar(a)=bar(i)+bar(j)+bar(k),bar(b)=bar(i)-2a^(2)bar(j)+bar(a) ,bar(c)=bar(i)+(a+1)bar(j)-abar(k) are linearly dependent vectors then the real 'a' lies in the interval.

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

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)=bar(i)+bar(j)+bar(k),bar(b)=4bar(i)+3bar(j)+4bar(k),bar(c)=bar(i)+alphabar(j)+betabar(k) are linearly dependent vectors and |bar(c)|=sqrt(3) then

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

The orthogonal projection of bar(a)=2bar(i)+3bar(j)+3bar(k) on bar(b)=bar(i)-2bar(j)+bar(k) (where bar(i)*bar(j)*bar(k) are unit vectors along there mutually perpendicular directions is

If there vectors bar(a)=bar(i)+bar(j)+bar(k) , bar(b)=bar(i)-2a^(2)bar(j)+abar(k) , bar(c)=bar(i)+(a+1)bar(j)-abar(k) are linearly dependent vectors then the real a lies in the interval.

If bar(a)=2bar(i)+3bar(j),bar(b)=bar(i)+bar(j)+bar(k),bar(c)=3bar(i)+lambdabar(j)+2bar(k) and [bar(a)bar(b)bar(c)]=-1 then lambda