# Vectors dot product and cross product help

In summary: Next, you can use the Pythagorean theorem to find the magnitude of [tex]A_x[/itex] and [tex]A_y[/itex].

## 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

Last edited:

## 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]

Where does the ex and ey come from?

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.

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.

## What is a vector?

A vector is a mathematical object that has both magnitude (or size) and direction. It is commonly represented by an arrow in two or three dimensions.

## What is the dot product of two vectors?

The dot product, also known as the scalar product, is a mathematical operation that takes two vectors and produces a scalar (a single number) as the result. It is calculated by multiplying the magnitudes of the two vectors and the cosine of the angle between them.

## What is the cross product of two vectors?

The cross product, also known as the vector product, is a mathematical operation that takes two vectors and produces a vector as the result. It is calculated by multiplying the magnitudes of the two vectors, the sine of the angle between them, and a unit vector perpendicular to both vectors.

## What is the significance of the dot product in physics?

The dot product is used in physics to calculate the work done by a force on an object, as well as the amount of energy transferred between two objects. It is also used in determining the angle between two vectors and in calculating the projections of one vector onto another.

## What is the significance of the cross product in physics?

The cross product is used in physics to calculate the torque (or rotational force) applied to an object, as well as the angular momentum of a rotating object. It is also used in determining the area of a parallelogram formed by two vectors and in calculating the direction of a magnetic field created by a current-carrying wire.

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