Question

1. For each sentence below, determine whether it is true (T) or false (F) by circling the corresponding letter. If the sentence is true, give a brief mathematical reason for your choice; if it is false, give an example to show it. ​

Answer 1

(a) True.
`\vec u* \vec v` is perpendicular to both
`\vec u` and
`\vec v`. So
`(\vec u* \vec v) \cdot \vec u = 0`.

(b) True. The cross product is anti-commutative, so
`\vec v * \vec u = -(\vec u* \vec v)`. The magnitude is the same either way,

`\|\vec u* \vec v\| = \| -(\vec v* \vec u)\| = |-1| \|\vec v* \vec u\| = \|\vec v * \vec u\|`

(c) False. The cross product of any unit vector with itself is the zero vector, which has magnitude zero.