The scalar triple product is 0.
If v = 4i - j and w = 6i + 7j - 4k, then their cross product is
v × w = (4i - j) × (6i + 7j - 4k)
v × w = 24 (i × i) + 28 (i × j) - 16 (i × k) - 6 (j × i) - 7 (j × j) + 4 (j × k)
v × w = 28k - 16 (-j) - 6 (-k) + 4i
v × w = 4i + 16j + 34k
and
u • (v × w) = (i + 4j - 2k) • (4i + 16j + 34k)
u • (v × w) = 4 + 64 - 68
u • (v × w) = 0
Yes, they are coplanar.
The vectors v and w together span a plane. v × w is a vector that is perpendicular to this plane. Since the dot product of u with this vector is 0, this means u is perpendicular to v × w, which in turn means that u is in the same plane as v and w.
