Let H = Span{V1,V2) and K = Span{V3,V4), where V1, V2, V3, and v4 are given below.
V1=
$$\begin{bmatrix} 1 \\ 7 \\ 8 \end{bmatrix}$$, V2=
$$\begin{bmatrix} 4 \\ 1 \\ 5 \end{bmatrix}$$, V3=
$$\begin{bmatrix} 5 \\ -1 \\ 1 \end{bmatrix}$$, V4=
$$\begin{bmatrix} 0 \\ -14 \\ -6 \end{bmatrix}$$
Then H and K are subspaces of R³. In fact, H and K are planes in R³ through the origin, and they intersect in a line through 0. Find a nonzero vector w that generates that line.
w=
[Hint: w can be written as c₁₁ + C2V2 and also as C3V3 + C4V4. To build w, solve the equation C₁₁ + C2V2 = C3V3+C4V4 for the unknown c's.]
