Vector Product

1. 1
Properties of the Vector Product
Determine whether these properties are true or not by looking at either
numerical examples first or using 𝒂 = 𝑥! 𝒊 + 𝑦! 𝒋 + 𝑧! 𝒌 and 𝒃 = 𝑥! 𝒊 + 𝑦! 𝒋 + 𝑧! 𝒌.
You must provide evidence for your answer.
Are the following true?
𝒂×𝒃 = 𝒃×𝒂
𝑘𝒂 ×𝒃 = 𝑘 𝒂×𝒃
𝒂× 𝒃 + 𝒄 = 𝒂×𝒃 + 𝒂×𝒄

2. 2
Justify and explain why or when
Can you justify and explain in words the following properties:
𝒂×𝒃 = 0 when…..
𝒂×𝒃 = 𝒂 𝒃 when…
Two vectors are parallel when
Two vectors are perpendicular when