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. $6 w \cdot 3 w$
A)vector
B)scalar

Question

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. $6 w \cdot 3 w$ ​
A)vector
B)scalar

Quizplus · Accepted Answer

The dot product of two vectors results in a scalar, and since both vectors are the same in this case (3w), the operation is scalar multiplication of the magnitude squared of vector w by 6, resulting in a scalar.

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

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