The points UUU, VVV, W W\,W and Z Z\,Z have position vectors u=6i−2j+k\mathbf{u} = 6\mathbf{i} - 2\mathbf{j} + \mathbf{k}u=6i−2j+k, v=2i+6j−7k\mathbf{v} = 2\mathbf{i} + 6\mathbf{j} - 7\mathbf{k}v=2i+6j−7k, w=−3i+5j+2k\mathbf{w} = -3\mathbf{i} + 5\mathbf{j} + 2\mathbf{k}w=−3i+5j+2k and z=3i−7j+14k\mathbf{z} = 3\mathbf{i} - 7\mathbf{j} + 14\mathbf{k}z=3i−7j+14k
Show that UV→\overrightarrow{UV}UV is parallel to WZ→\overrightarrow{WZ}WZ