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

Printable View

- Feb 16th 2009, 12:56 PMbluebiroVector question.
Find u such that the vectors i + j - k, 2i - j + k and ui - j + uk are coplanar.

- Feb 16th 2009, 01:33 PMPlato
Solve $\displaystyle \left\langle {u, - 1,u} \right\rangle \cdot \left[ {\left\langle {1,1, - 1} \right\rangle \times \left\langle {2, - 1,1} \right\rangle } \right] = 0$ for u.

- Feb 16th 2009, 02:25 PMHallsofIvy
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.