is a vector, with its direction perpendicular to both
→
A
and
→
B
.
→
A
×
→
B
is area. If side B is zero, area is zero.
→
A
×0 is a zero vector. If in case 0 is a scalar, then also the product is zero. But a scalar × a vector is also a vector.Hence one gets a zero vector in any case.