Given vectors $\mathbf { u } = \left\langle u _ { 1 } , u _ { 2 } \right\rangle , \mathbf { v } = \left\langle v _ { 1 } , v _ { 2 } \right\rangle$, and $\mathbf { w } = \left\langle w _ { 1 } , w _ { 2 } \right\rangle$, determine whether the result of the following expression is a vector or a scalar.
$\mathbf { u } \cdot \mathbf { w } + \mathbf { v } \cdot \mathbf { w }$
A) vector
B) scalar

Question

Quizplus · Accepted Answer

The expression involves dot products ($\mathbf{u} \cdot \mathbf{w}$ and $\mathbf{v} \cdot \mathbf{w}$), each of which results in a scalar. The sum of two scalars is also a scalar.

Given Vectors u=⟨u1,u2⟩,v=⟨v1,v2⟩\mathbf { u } = \left\langle u _ { 1 } , u _ { 2 } \right\rangle , \mathbf { v } = \left\langle v _ { 1 } , v _ { 2 } \right\rangleu=⟨u1​,u2​⟩,v=⟨v1​,v2​⟩

Given Vectors $\mathbf { u } = \left\langle u _ { 1 } , u _ { 2 } \right\rangle , \mathbf { v } = \left\langle v _ { 1 } , v _ { 2 } \right\rangle$