Question

find the indicated quantity, given ( mathbf{u}=(6,4), mathbf{v}=(-6,-1) ).
step 4 of 4: find ( (mathbf{u} cdot mathbf{v}) 5 mathbf{v} ).

Explanation:

Step1: Calculate the dot product \( \mathbf{u}\cdot\mathbf{v} \)

The dot product of two vectors \( \mathbf{u}=\langle u_1,u_2
angle \) and \( \mathbf{v}=\langle v_1,v_2
angle \) is given by \( \mathbf{u}\cdot\mathbf{v}=u_1v_1 + u_2v_2 \).
For \( \mathbf{u}=\langle6,4
angle \) and \( \mathbf{v}=\langle - 6,-1
angle \), we have \( \mathbf{u}\cdot\mathbf{v}=(6\times(-6))+(4\times(-1))=-36 - 4=-40 \).

Step2: Calculate \( (\mathbf{u}\cdot\mathbf{v})5\mathbf{v} \)

First, find \( 5\mathbf{v} \). If \( \mathbf{v}=\langle - 6,-1
angle \), then \( 5\mathbf{v}=\langle5\times(-6),5\times(-1)
angle=\langle - 30,-5
angle \).
Now, multiply the scalar \( \mathbf{u}\cdot\mathbf{v}=-40 \) with the vector \( 5\mathbf{v}=\langle - 30,-5
angle \).
\((\mathbf{u}\cdot\mathbf{v})5\mathbf{v}=-40\langle - 30,-5
angle=\langle(-40)\times(-30),(-40)\times(-5)
angle=\langle1200,200
angle \)

Answer:

\(\langle1200,200
angle\)