Question

if $\mathbf{u}=\langle -5,7\
angle$, $\mathbf{v}=\langle -3,6\
angle$, and $\mathbf{w}=\langle -11,2\
angle$, evaluate $\mathbf{u}\cdot(\mathbf{v}+\mathbf{w})$.

a. 134
b. 126
c. 107
d. 116

Explanation:

Step1: Calculate \(v + w\)

For vectors \(v=\langle - 3,6
angle\) and \(w=\langle - 11,2
angle\), vector addition is \(\langle x_1 + x_2,y_1 + y_2
angle\).
\(v + w=\langle-3+( - 11),6 + 2
angle=\langle-14,8
angle\)

Step2: Calculate the dot - product \(u\cdot(v + w)\)

For vectors \(u=\langle - 5,7
angle\) and \(v + w=\langle-14,8
angle\), the dot - product formula is \(u\cdot(v + w)=u_1(v + w)_1+u_2(v + w)_2\).
\(u\cdot(v + w)=(-5)\times(-14)+7\times8\)
\(=70 + 56\)

Answer:

\(126\), so the answer is B.