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seropon [69]
2 years ago
14

Let $$\mathbf { u } , \mathbf { v } , \text { and } \mathbf { w }$$ be vectors. Which of the following make sense, and which do

not? Give reasons for your answers. $$
a.( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { w }\quad
b. \mathbf { u } \times ( \mathbf { v } \cdot \mathbf { w } )\ quad
c. \mathbf { u } \times ( \mathbf { v } \times \mathbf { w } )\quad
d. \mathbf { u } \cdot ( \mathbf { v } \cdot \mathbf { w } ).$$
Mathematics
1 answer:
Daniel [21]2 years ago
5 0

(<em>u</em> × <em>v</em>) • <em>w</em> makes sense, since <em>u</em> × <em>v</em> is another vector, and so (<em>u</em> × <em>v</em>) • <em>w</em> is a scalar.

<em>u</em> × (<em>v</em> • <em>w</em>) does not make sense, since <em>v</em> • <em>w</em> is a scalar, and the cross product is not defined between a vector and a scalar.

(<em>u</em> × <em>v</em>) × <em>w</em> makes sense, since <em>u</em> × <em>v</em> is a vector and so is <em>w</em>.

<em>u</em> • (<em>v</em> • <em>w</em>) does not make sense, since <em>v</em> • <em>w</em> is scalar, and the dot product is not defined between a vector and a scalar.

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