Solve for vectors A and B, where
`A+B=a,AxxB=b,A*a=1`.

Solve for matrics A and B , where 2A + B = [{:( 3,-4),(2,7) :}] and A - 2B =[{:( 4,3),(1,1):}]

The vectors a,b and a+b are

Solve for vec x,vecx xx vec b=veca , where veca,vecb are two given vectors such that veca is perpendicular to vecb .

Solve the cryptarithm: A B \ X\ A B =\ A C B

If theta is the abgle between two vectors A and B , then match the following two columns. {:(,"Column I ",,"Column II"),((A),A.B=|AxxB|,(P),theta=90^(@)),((B),A.B=B^(2),(Q),theta=0^(@)or 180^(@)),((C),|A+B|=|A-C|,(r),A=B),((D), |AxxB|=AB,(s),"None"):}

The resultant of two vectors A and B is perpendicular to the vector A and its magnitude is equal to half the magnitude of vector B. The angle between A and B is -

If A={a ,b} and B={3}, find AxxB

Let A={-1,3,5} and B={2,3} find AxxB

If a, b, c are three given non-coplanar vectors and any arbitratry vector r is in space, where Delta_1=|[r*a, b*a, c*a], [r*b, b*b, c*b], [r*c, b*c, c*c]| : Delta_2=|[a*a, r*a, c*a], [a*b, r*b, c*b], [a*c, r*c, c*c]| Delta_3=|[a*a, b*a, r*a], [a*b, b*b, r*b], [a*c, b*c, r*c]|, Delta_4=|[a*a, b*a, c*a], [a*b, b*b, c*b], [a*c, c*c, c*c]| Q. The vector r is expressible in the form

If a, b and c are any three vectors and their inverse are a^(-1), b^(-1) and c^(-1) and [a b c]ne0 , then [a^(-1) b^(-1) c^(-1)] will be