Question

if ( mathbf{u}=langle-3,5
angle ) and ( mathbf{v}=langle 4,4
angle ), evaluate ( (2 mathbf{u}) cdot mathbf{v} ).

a. 12
b. 22
c. 52
d. 16

Explanation:

Step1: Calculate \(2\mathbf{u}\)

Multiply each component of \(\mathbf{u}=\langle - 3,5
angle\) by \(2\).
\(2\mathbf{u}=2\langle -3,5
angle=\langle2\times(-3),2\times5
angle=\langle - 6,10
angle\)

Step2: Calculate the dot - product \((2\mathbf{u})\cdot\mathbf{v}\)

If \(\mathbf{a}=\langle x_1,y_1
angle\) and \(\mathbf{b}=\langle x_2,y_2
angle\), then \(\mathbf{a}\cdot\mathbf{b}=x_1x_2 + y_1y_2\).
Here, \(2\mathbf{u}=\langle - 6,10
angle\) and \(\mathbf{v}=\langle4,4
angle\), so \((2\mathbf{u})\cdot\mathbf{v}=(-6)\times4+10\times4\)
\(=(- 24)+40\)
\(=16\)

Answer:

D. \(16\)