" Let "a,b>0" and "vec u=(hat i)/(a)+(4hat j)/(b)+bhat k" and "vec beta=bhat i+ahat j+(1)/(b)hat k," then the maximum value uf "(10)/(5+vec alpha.vec beta)" is "

* Let a,b>0 and vec alpha=(hat i)/(a)+4(hat j)/(b)+bhat k and beta=bhat i+ahat j+(hat k)/(b) then the maximum value of (30)/(5+alpha*beta)

Taking vec a= 2 hat i-3 hat j- hat k and vec b=hat i+4 hat j-2 hat k , verify that vec a * vec b = vec b*vec a .

If vec a=3 hat i+4 hat j and vec b=hat i-hat j+hat k , find the value of | vec a*vec b|.

If vec a=3hat i+4hat j and vec b=hat i+hat j+hat k, find the value of |vec a xxvec b|

If vec a=5 hat i-hat j-3 hat k and vec b=hat i+3 hat j -5 hat k , then show that the vecctors vec a+vec b and vec a-vec b are perpendicular.

If vec A = 2 hat i + 2 hat j - hat k and vec B = hat i + 4 hat j- 3 hat k then find (a) vec A * vec B (b) vec A xx vec B

vec a = (hat i + hat j + hat k), vec a * vec b = 1 and vec a xxvec b = hat j-hat k. Then vec b is

If vec a = 5 hat i - hat j - 3 hat k and vec b = hat i + 3 hat j - 5 hat k , then show that the vectors vec a + vec b and vec a - vec b are orthogonal

Let vec alpha=ahat i+bhat j+chat k,vec beta=bhat i+chat j+ahat k and vec gamma=chat i+ahat j+bhat k are three coplanar vectors with a!=b, and vec v=hat i+hat j+hat k . Then v is perpendicular to vec alpha b.vec beta c.vec gamma d.none of these

Let vec a=5 hat i- hat j+7 hat k and vec b= hat i- hat j+lambda hat k . Find lambda such that vec a+ vec b is orthogonal to vec a- vec bdot