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`

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))=

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)+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))|=

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 quad 2bar(i)+bar(j)-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))=(1+alpha)bar(i)+beta(1+alpha)bar(j)+gamma(1+alpha)(1+beta) then

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

If =2bar(i)-bar(j)+3bar(k),b=-bar(i)+4bar(j)-2bar(k),bar(c)=5bar(i)+bar(j)+7bar(k) and xbar(a)+ybar(b)=bar(c) then (x,y)=(A)(3,1)(B)(3,-1) (C) (-3,1)(D)(-3,-1)

If bar(a)=a_(1)bar(i)+b_(1)bar(j)+c_(1)bar(k),bar(b)=a_(2)bar(i)+b_(2)bar(j)+c_(3)bar(k) ,then bar(a)*bar(b)

Given three vectors bar(a)=6bar(i)-3bar(j),bar(b)=2bar(i)-6bar(j) and bar(c)=-2bar(i)+21bar(j) such that bar(alpha)=bar(a)+bar(b)+bar(c) Then the resolution of the vector bar(alpha) into components with respect to bar(a) and bar(b) given by