Question

let
u = 2i - j, v = 5i + j, w = i + 3j
find the specified scalar.
u·(v + w)
u·(v + w) = \square

Explanation:

Step1: Calculate $\boldsymbol{v+w}$

Add corresponding components:
$\boldsymbol{v+w}=(5\boldsymbol{i}+\boldsymbol{j})+(\boldsymbol{i}+3\boldsymbol{j})=(5+1)\boldsymbol{i}+(1+3)\boldsymbol{j}=6\boldsymbol{i}+4\boldsymbol{j}$

Step2: Compute dot product $\boldsymbol{u}\cdot(\boldsymbol{v+w})$

Multiply corresponding components and sum:
$\boldsymbol{u}\cdot(\boldsymbol{v+w})=(2\boldsymbol{i}-\boldsymbol{j})\cdot(6\boldsymbol{i}+4\boldsymbol{j})=(2\times6)+(-1\times4)$

Step3: Simplify the expression

Calculate the arithmetic:
$(2\times6)+(-1\times4)=12-4=8$

Answer:

8