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.
Work Step by Step
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.
