# Math Help - Vector question.

1. ## Vector question.

Find u such that the vectors i + j - k, 2i - j + k and ui - j + uk are coplanar.

2. Solve $\left\langle {u, - 1,u} \right\rangle \cdot \left[ {\left\langle {1,1, - 1} \right\rangle \times \left\langle {2, - 1,1} \right\rangle } \right] = 0$ for u.

3. Or: three vectors are co-planar if any one of them can be written as a linear combination of the other two.

Find a u such that a(i + j - k)+ b(2i - j + k)= ui - j + uk for some a and b. That is, a+ 2b= u, a- b= -1, -a+b= u. You can solve the first and second equations for a and u in terms of b, then find b so that the second equation is satisfied.