Prove that if a × x = 0 for all x ∈ℝ3, then a = 0. (Hint: Exercise 1 or 2.)
Exercise 1–2
1. Verify that for any vector a = a1i+ a2j+ a3k,
2. Show that for any vector a = a1i+ a2j+ a3k,
(Hint: Exercise 1 and Figure.)
Figure.
Mnemonoic for remembering the cross product of the basis vectors
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