Use the vectors $\mathbf { u } = \langle 2,2 \rangle$ , $\mathbf { v } = \langle - 2,2 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar. $3 \mathbf { u } \cdot \mathbf { v }$
A) $\langle 0,2 \rangle$ ; vector
B)-2; scalar
C)2; scalar
D) $\langle 4 , - 4 \rangle$ ; vector
E)0; scalar

Question

Use the vectors $\mathbf { u } = \langle 2,2 \rangle$ , $\mathbf { v } = \langle - 2,2 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar.   $3 \mathbf { u } \cdot \mathbf { v }$  
A) $\langle 0,2 \rangle$ ; vector
B)-2; scalar
C)2; scalar
D) $\langle 4 , - 4 \rangle$ ; vector
E)0; scalar

Quizplus · Accepted Answer

The result of $3 \mathbf { u } \cdot \mathbf { v }$ is a scalar because the dot product of two vectors is a scalar. Calculating $3(\mathbf { u } \cdot \mathbf { v }) = 3((2)(-2) + (2)(2)) = 3(0) = 0$.

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

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