Question

Evaluate the expression.

r = <5, 9, -4>, v = <3, 3, -8>, w = <9, -6, -1>

v ⋅ w

<-15, -27, -32>
0
17
<27, -18, 8>

Answer 1

Given two vectors \(a=\langle a_1,a_2\rangle\) and \(b=\langle b_1,b_2\rangle\), the dot product of \(a\) and \(b\) is
\[a\bullet b=\langle a_1,a_2\rangle\bullet\langle b_1,b_2\rangle=a_1b_1+a_2b_2\]

Answer 2

In three dimensions, the premise is the same.
\[v\bullet w=v_1w_1+v_2w_2+v_3w_3\]
Note that this will not give you a vector as a result, so you can eliminate the first and last options.