## Calculus 8th Edition

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.
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.