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]

 

[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.

 

[paranormal]

by multiplying Bx and By by 5 and using the equation.
It seems like you are on the right track! To find the magnitude of vector B, you can use the Pythagorean theorem as you did. However, it is important to note that the magnitude of a vector is always positive, so the magnitude of vector B would be 12, not -12.

For part a), you are correct in multiplying the magnitude and angle of vector A by 5 and then using the dot product equation. This will give you the scalar value of the dot product.

For part b), to find the cross product, you can use the formula: A x B = (AyBz - AzBy)i + (AzBx - AxBz)j + (AxBy - AyBx)k. In this case, you would substitute the values of vector A and B and then multiply the result by 4. This will give you the vector in unit vector notation.

To convert the vector into magnitude angle notation, you can use the formula: |A| = √(Ax^2 + Ay^2 + Az^2). This will give you the magnitude of the vector. Then, you can use the formula: tan^-1(Ay/Ax) to find the angle. In this case, you would need to substitute the values of the cross product vector you found and then multiply the result by 3 to get the final magnitude and angle in spherical coordinates.

I hope this helps! Let me know if you have any other questions.