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

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))

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

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))|=

bar(a)=2bar(i)+bar(i)+bar(k),bar(b)=bar(i)+2bar(j)+2bar(k),bar(c)=bar(i)+bar(j)+2bar(k) and bar(a)xx(bar(b)xxbar(c))=

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)

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.

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

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.

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