Use the vectors $\mathbf { u } = \langle 2,4 \rangle$ , $\mathbf { v } = \langle - 5,3 \rangle$ and $\mathbf { w } = \langle 3 , - 1 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar.
$\left( \mathbf { v } ^ { * } \mathbf { u } \right) - \left( \mathbf { w } ^ { \cdot } \mathbf { v } \right)$
A)16; scalar
B) $\langle 24,16 \rangle$ ; vector
C) $\langle 0,20 \rangle$ ; vector
D)22; scalar
E)20; scalar

Question

Use the vectors $\mathbf { u } = \langle 2,4 \rangle$ , $\mathbf { v } = \langle - 5,3 \rangle$ and $\mathbf { w } = \langle 3 , - 1 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar.
  $\left( \mathbf { v } ^ { * } \mathbf { u } \right) - \left( \mathbf { w } ^ { \cdot } \mathbf { v } \right)$  
A)16; scalar
B) $\langle 24,16 \rangle$ ; vector
C) $\langle 0,20 \rangle$ ; vector
D)22; scalar
E)20; scalar

Quizplus · Accepted Answer

The expression involves the dot product of vectors, which results in a scalar. The calculation is $(\mathbf{v} \cdot \mathbf{u}) - (\mathbf{w} \cdot \mathbf{v}) = ((-5)(2) + (3)(4)) - ((3)(-5) + (-1)(3)) = (-10 + 12) - (-15 - 3) = 2 - (-18) = 20$.

Use the Vectors u=⟨2,4⟩\mathbf { u } = \langle 2,4 \rangleu=⟨2,4⟩

Use the Vectors $\mathbf { u } = \langle 2,4 \rangle$