If the vectors `bar(a)=2bar(i)-bar(j)+bar(k)`,`bar(b)=bar(i)+2bar(j)-3bar(k)` and `bar(c)=3bar(i)+pbar(j)+5bar(k)` are coplanar,then find `P`

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

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 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 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 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

The number of distinct real values of lambda for which the vectors - lambda^(2)bar(i)+bar(j)+bar(k),bar(i)-lambda^(2)bar(j)+bar(k) and bar(i)+bar(j)-lambda^(2)bar(k) are coplanar

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))

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))=