Vectors dot product and cross product help

[maximade]

Homework Statement

Vectors A and B (both with the lines over it) lie in an xy plane. Vector A has magnitude 8 and angle 130 degrees, Vector B has components Bx=-7.72 and By=-9.2.
a)What is 5(vector A) dot vector B?
b)What is 4(Vector A) cross 3(vector B) in unit vector notation and magnitude angle notation with spherical coordinates?

Homework Equations

Vector A dot Vector B=abcos(phi)
Other vector equations that can apply to this that I don't know maybe...

The Attempt at a Solution

I figured that I try to find the vector B by doing the Pythagorean theorem with the two components of B and I get -12 as magnitude. After that I'm not even sure what to do, like for the 5(vector A) do I multiply the angle and magnitude by 5 then do the Vector A dot Vector B=abcos(phi) equation? Same question applies to b and how do I turn the magnitude and the angle into unit vector notation and magnitude angle notation? Thanks in advance.

EDIT: Forget A, I solved it

 

[gabbagabbahey]

Homework Statement

Vectors A and B (both with the lines over it) lie in an xy plane. Vector A has magnitude 8 and angle 130 degrees, Vector B has components Bx=-7.72 and By=-9.2.
a)What is 5(vector A) dot vector B?
b)What is 4(Vector A) cross 3(vector B) in unit vector notation and magnitude angle notation with spherical coordinates?

Homework Equations

Vector A dot Vector B=abcos(phi)
Other vector equations that can apply to this that I don't know maybe...

The Attempt at a Solution

I figured that I try to find the vector B by doing the Pythagorean theorem with the two components of B and I get -12 as magnitude. After that I'm not even sure what to do, like for the 5(vector A) do I multiply the angle and magnitude by 5 then do the Vector A dot Vector B=abcos(phi) equation? Same question applies to b and how do I turn the magnitude and the angle into unit vector notation and magnitude angle notation? Thanks in advance.

EDIT: Forget A, I solved it

The easiest way to do part b) is to start by finding [tex]A_x[/itex] and [tex]A_y[/itex]. As a hint on finding those components, consider [tex]\vec{A}\cdot\vec{e}_x[/itex] and [tex]\vec{A}\cdot\vec{e}_y[/itex] <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f609.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":wink:" title="Wink :wink:" data-smilie="2"data-shortname=":wink:" />[/tex][/tex][/tex][/tex]

 

[maximade]

Where does the ex and ey come from?

 

[gabbagabbahey]

Where does the ex and ey come from?

I'm using them to represent the Cartesian unit vectors. You might be more used to seeing i and j...different authors use different notations for the same quantities, so it's worth familiarizing yourself with common notations.