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.
$( w \cdot w ) w$
A) vector
B) scalar

Question

Quizplus · Accepted Answer

The expression $( w \cdot w ) w$ involves the dot product of $\mathbf{w}$ with itself, which yields a scalar, and then multiplies this scalar by the vector $\mathbf{w}$. Multiplying a scalar by a vector results in a vector, hence the expression is a vector.

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