Question

If u=<7,2> and v=<2,-3> find u + v, u-v and u*v

Answer 1

vectorsFirst, we express each vector as rectangular form

$\begin{gathered} u=7i+2j \\ v=2i-3j \end{gathered}$

Now, we proceed to add them

$u+v=(7i+2j)+(2i-3j)$

When we add (or subtract) vectors, we have to operate the corresponding coordinates.

$u+v=(7i+2i)+(2j-3j)=9i-j$

So, the sum u+v is equal to <9,-1>.

Then, we subtract the vects.

$\begin{gathered} u-v=(7i+2j)-(2i-3j)=7i+2j-2i+3j \\ u-v=5i+5j \end{gathered}$

So, the subtraction u-v is <5,5>.

At last, we solve the dot product.

$\begin{gathered} u\cdot v=(7i+2j)\cdot(2i-3j)=(7\cdot2)i+(2\cdot(-3))j \\ u\cdot v=14i-6j \end{gathered}$

Therefore, the dot product u*v is equal to <14,-6>.