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True/False: Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: For any two vectors u and v in ${\mathrm{鈩�}}^3$, $u脳v=v脳u$.

(b) True or False: If u and v are two vectors in ${\mathrm{鈩�}}^3$, then $u脳v=u路v$.

(c) True or False: If $u脳v=v脳u$, then u and v are parallel.

(d) True or False: If u, v, and w are vectors in R3, then (u 脳 v) 脳 w = u 脳 (v 脳 w).

(e) True or False: The triple scalar product can be used to find the volume of a parallelepiped.

(f) True or False: If u, v, and w are vectors in R3, then u 路 (v 脳 w) = 鈭抳 路 (u 脳 w).

(g) True or False: If u and v are nonparallel vectors in R3, then u 路 v u脳v = cot 胃, where 胃 is the angle between u and v.

(h) True or False: If u and v are unit vectors in R3, then u 脳 v is also a unit vector.

Step by step solution

01

Step 1. Given informaton:

a

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