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.
$\mathbf { u } \cdot 4 \mathrm { v }$
A) vector
B) scalar

Question

Quizplus · Accepted Answer

The dot product of two vectors is always a scalar, and multiplying a vector by a scalar results in a vector. Therefore, the result of $\mathbf { u } \cdot 4 \mathrm { v }$ will be a scalar multiplied by a scalar, which is still 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 $\mathbf { u } = \left\langle u _ { 1 } , u _ { 2 } \right\rangle , \mathbf { v } = \left\langle v _ { 1 } , v _ { 2 } \right\rangle$