Question

Given v = 5i + j and w= i + 5j, find the following.a) v.wb) v•v

Answer 1

We have the vectors:

$\begin{gathered} v=(v_1,v_2)=(5,1), \\ w=(w_1,w_2)=(1,5)\text{.} \end{gathered}$

a) We compute the dot product v•w:

$v\cdot w=(v_1,v_2)\cdot(w_1,w_2)=v_1\cdot w_1+v_2\cdot w_2=5\cdot1+1\cdot5=10.$

b) v•v

$v\cdot v=(v_1,v_2)\cdot(v_1,v_2)=v_1\cdot v_1+v_2\cdot v_2=5\cdot5+1\cdot1=25+1=26.$

Answers

a) v•w = 10

b) v•v = 26