If `vec(a) = alpha hat(i) + beta hat(j)+ 3 hat(k)`,
`vec(b) = - beta hat(i) - alpha hat(j) - hat(k) ` and
`vec( c ) = hat(i) - 2hat(j) - hat(k)`
such that `vec( a) . vec(b) =1` and `vec( b ).vec(c ) = - 3` then `(1)/(3) ((vec(a) xx vec(b)).vec( c))` is equal to `"________"`.

Let vec(a) = hat(i) - alpha hat(j) + beta hat(k) , vec(b) = 3 hat(i) + beta hat(j) - alpha hat(k) and vec(c) = - alpha hat(i) - 2 hat(j) + hat(k) , where alpha and beta are integers. If vec(a)* vec(b) = - 1 and vec(b) * vec(c) = 10 " then " ( vec(a) xx vec(b)) * vec(c) is equal to _____

If vec(a) = hat(i) + hat(j) + 2 hat(k) and vec(b) = 3 hat(i) + 2 hat(j) - hat(k) , find the value of (vec(a) + 3 vec(b)) . ( 2 vec(a) - vec(b)) .

If vec(a) = hat(i) + hat(j) + hat(k), vec(b) = hat(i) - hat(j) + hat(k) and vec(c )= hat(i) + hat(j) - hat(k) , then what is vec(a) xx (vec(b)+ vec(c )) + vec(b) xx (vec(c ) + vec(a)) + vec(c ) xx (vec(a) + vec(b)) is equal to ?

Let vec(a) = hat(i) + hat(j) + hat(k),vec(b) = hat(i) - hat(j) + 2hat(k) and vec(c) = xhat(i) + (x-2)hat(j) - hat(k) . If the vector vec(c) lies in the plane of vec(a) and vec(b) then x equals

If vec(a) = 3 hat(i) + 2 hat(k) , vec(b) = 3hat(j) - hat(k) and vec(c ) = hat(i) + hat(j) + hat(k) . Find ( vec(a) xx vec(b)). vec(c ) .

If vec(a) = 2 hat(i) + 2 hat(j) + hat(k) , vec(b) = - hat(i) + hat(j) + 2 hat(k) and vec ( c) = 3 hat(i) + hat(j) such that vec(a) + lambda hat (b) is perpendicular to vec( c) , find lambda .

If vec(a)= hat(i) - 2hat(j) + 5hat(k) and vec(b) = 2hat(i) + hat(j) -3hat(k) , then (vec(b) - vec(a)).(3 vec(a) +vec(b)) equal to?

Let vec(a) = hat(i) + hat(j) + hat(k), vec(b) = hat(i) - hat(j) + 2hat(k) and vec(c) = xhat(i) + (x-2)hat(j) - hat(k) . If the vector vec(c) lies in the plane of vec(a) & vec(b) , then x equals

If vec(a) = hat(i)- hat(k) , vec(b) = x hat(i) + hat(j) + (1-x) hat(k), vec(c ) = y hat(i) + x hat(j) + (1+ x- y)hat(k) then vec(a).(vec(b) xx vec(c )) depends on

If vec(a)= hat(i) - 2hat(j) + 5hat(k), vec(b)= 2hat(i) +hat(j)- 3hat(k) then what is (vec(a)- vec(b)).(3 vec(a) +vec(b)) equal to ?