#### Answer

1. The cross product can be used to test if the two vectors are scalar multiplies of each other, that is, parallel to each other
$a \times b =0$ iff a and b are scalar multiples.
2. If the magnitude of $a$ (that is, $|a|$) and the magnitude of $b$ (that is, $|b|$) is known and the angle between $a$ and $b$ (that is, $\theta$) is to be known, the product of the magnitudes and the sine of the angle is the cross product of $a$ and $b$.
$a \times b= |a| |b| sin \theta$
3. The cross product is used to calculate the area of a parallelogram of two vectors.