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)`

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))|=

Let a=alpha_(1)bar(i)+alpha_(2)bar(j)+alpha_(3)bar(k),bar(b)=beta_(1)bar(i)+beta_(2)bar(j)+beta_(3)kbar( and )bar(c)=gamma_(1)bar(i)+gamma_(2)bar(j)+gamma_(3)bar(k),|bar(a)|=2sqrt(2), makes an angle (pi)/(3) with the plane of bar(b),bar(c) and the angle between bar(b),bar(c) is (pi)/(6), then det[[alpha_(1),alpha_(2),alpha_(3)beta_(1),beta_(2),beta_(3)]] is equal to (n is even natural number)

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)+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

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(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 bar(a)=2bar(i)-3bar(j)+6bar(k) , bar(b)=-2bar(i)+2bar(j)-bar(k) and k =(the projection of bar(a) on bar(b)) /(the projection of bar(b) on bar(a)) then the value of 3k=

If bar(a)=2bar(i)-3bar(j)+6bar(k), bar(b)=-2bar(i)+2bar(j)-bar(k) and lambda=(the projection of bar(a) on bar(b))/( the projection of bar(b) on bar(a)) then the value of lambda is

If [bar(a)+2bar(b)2bar(b)+bar(c)5bar(c)+bar(a)]=k[bar(a)bar(b)bar(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))=