# Help pls find vector b given a = 5i +j, a dot b = 12, and the angle between a and b is 58 degrees (1 Viewer)

#### Interdice

##### Well-Known Member
All I managed to get out of this is that

cos(58) = 12/(5x + y)

#### Drongoski

##### Well-Known Member
Wonder if answers approx:

0.926 + 2.451 i and 1.797 - 1.906 i

#### Interdice

##### Well-Known Member
looking at the answers it is actually b = 3i -3j or b = 1.6i + 4.2j.

NEed some help figuring out how to get to the answers

#### tywebb

##### dangerman
I think we will be doing this:

$\bg_white |\overrightarrow{a}|=\sqrt{5^2+1^2}=\sqrt{26},\overrightarrow{b}=x\overrightarrow{i}+y\overrightarrow{j},|\overrightarrow{b}|=\sqrt{x^2+y^2}$

$\bg_white \overrightarrow{a}\cdot\overrightarrow{b}=5x+y=12$

$\bg_white \cos58^\circ=\frac{\overrightarrow{a}\cdot{\overrightarrow b}}{|\overrightarrow{a}||\overrightarrow{b}|}=\frac{12}{\sqrt{26x^2+26y^2}}$

At this point I think you can solve it but I put the equations in wolframalpha in the following way:

5x+y=12 and cos(58 degrees)=12/sqrt(26x^2+26y^2)

and got this:

$\bg_white \text{So }\overrightarrow{b}\approx1.56908\overrightarrow{i}+4.15462\overrightarrow{j}\text{ or }3.04631\overrightarrow{i}-3.23154\overrightarrow{j}$

Last edited:

#### Drongoski

##### Well-Known Member
I got |b| = 2.618 . . . instead of 4.441 . . ..
With this correction,(multiplying my answers by 4.441/2.618) should end up with roughly the same answer.