Use the vectors $\mathbf { u } = \langle 2,4 \rangle$ , $\mathbf { v } = \langle - 4,5 \rangle$ , and $\mathbf { w } = \langle 5 , - 4 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar.
$( \mathbf { u } \cdot 2 \mathbf { v } ) \mathbf { w }$
A)-96; scalar
B) $\langle 120 , - 92 \rangle$ ; vector
C) $\langle 120 , - 94 \rangle$ ; vector
D) $\langle 120 , - 100 \rangle$ ; vector
E) $\langle 120 , - 96 \rangle$ ; vector

Question

Use the vectors $\mathbf { u } = \langle 2,4 \rangle$ , $\mathbf { v } = \langle - 4,5 \rangle$ , and $\mathbf { w } = \langle 5 , - 4 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar.
  $( \mathbf { u } \cdot 2 \mathbf { v } ) \mathbf { w }$  
A)-96; scalar
B) $\langle 120 , - 92 \rangle$ ; vector
C) $\langle 120 , - 94 \rangle$ ; vector
D) $\langle 120 , - 100 \rangle$ ; vector
E) $\langle 120 , - 96 \rangle$ ; vector

Quizplus · Accepted Answer

The result is a vector because the dot product $\mathbf{u} \cdot 2\mathbf{v}$ yields a scalar, which when multiplied by vector $\mathbf{w}$, results in a vector. Calculation: $\mathbf{u} \cdot 2\mathbf{v} = \langle 2,4 \rangle \cdot \langle -8,10 \rangle = (2 \times -8) + (4 \times 10) = -16 + 40 = 24$. Then, $24\mathbf{w} = 24 \langle 5, -4 \rangle = \langle 120, -96 \rangle$.

Use the Vectors u=⟨2,4⟩\mathbf { u } = \langle 2,4 \rangleu=⟨2,4⟩

Use the Vectors $\mathbf { u } = \langle 2,4 \rangle$