Two vectors A and B lie in the same plane and it is given that |A|=1 and A.B=3. I have to find, in terms of A and B, the vector u, parallel to A, and the vector V perpendicular to A. Both of these vectors lie in the same plane such that u+v=A+B. u=4a and v=-3a+b.
The vector c is not parallel with the plane such that C.A=2 and C.B=-2. Given that |b| = 5. I have to find, in terms of A,B and C, vectors U,V and W such that U and V are respectively parallel to u and v and W is perpendicular to the plane in which A,B,C,u,v,U and V lie. Furthermore W + V + U = A + B + C
I have tried assigning scalars to U and V based on the equations for u and v. I have also set W=dA.eB.fC where d,e and f are scalars. I have then said W.B=0 as the two vectors must be perpendicular and then used the values of the crosses for which we have values to derive the equation 3d+25e+2f=0 and then tried to equate coefficients, but this has proved futile.
Any pointers would be greatly appreciated! Thanks.