Use the vectors $\mathbf { u } = \langle 3,5 \rangle$ , $\mathbf { v } = \langle - 2,2 \rangle$ , and $\mathbf { w } = \langle 5 , - 3 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar.
$( 3 \mathbf { w } \cdot \mathbf { v } ) \mathbf { u }$
A) $\langle - 144 , - 236 \rangle$ ; vector
B) $\langle - 144 , - 242 \rangle$ ; vector
C) $\langle - 144 , - 240 \rangle$ ; vector
D)-240; scalar
E) $\langle - 144 , - 244 \rangle$ ; vector

Question

Use the vectors $\mathbf { u } = \langle 3,5 \rangle$ , $\mathbf { v } = \langle - 2,2 \rangle$ , and $\mathbf { w } = \langle 5 , - 3 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar.
  $( 3 \mathbf { w } \cdot \mathbf { v } ) \mathbf { u }$ 
A) $\langle - 144 , - 236 \rangle$ ; vector
B) $\langle - 144 , - 242 \rangle$ ; vector
C) $\langle - 144 , - 240 \rangle$ ; vector
D)-240; scalar
E) $\langle - 144 , - 244 \rangle$ ; vector

Quizplus · Accepted Answer

The result is a vector because the dot product $(3\mathbf{w} \cdot \mathbf{v})$ yields a scalar, which is then multiplied by the vector $\mathbf{u}$, resulting in a vector. To find the correct answer, first calculate the dot product $3\mathbf{w} \cdot \mathbf{v}$, then multiply the result by $\mathbf{u}$.

Use the Vectors u=⟨3,5⟩\mathbf { u } = \langle 3,5 \rangleu=⟨3,5⟩

Use the Vectors $\mathbf { u } = \langle 3,5 \rangle$