Question

find the indicated quantity, given (mathbf{u}=langle 6,4
angle,mathbf{v}=langle -6,-1
angle step1 of2: find (2mathbf{u}cdotmathbf{v}).

Explanation:

Step1: Multiply vector \(u\) by scalar \(5\)

Given \(u=\langle6,4
angle\), then \(5u = 5\langle6,4
angle=\langle5\times6,5\times4
angle=\langle30,20
angle\).

Step2: Calculate the dot - product of \(5u\) and \(v\)

Given \(v = \langle-6,-1
angle\), the dot - product formula for two vectors \(\vec{a}=\langle a_1,a_2
angle\) and \(\vec{b}=\langle b_1,b_2
angle\) is \(\vec{a}\cdot\vec{b}=a_1b_1 + a_2b_2\).
For \(5u=\langle30,20
angle\) and \(v=\langle-6,-1
angle\), we have \((5u)\cdot v=(30)\times(-6)+(20)\times(-1)\).
First, calculate \(30\times(-6)=- 180\) and \(20\times(-1)=-20\).
Then, \((5u)\cdot v=-180-20\).

Answer:

\(-200\)