Vector Addition of Components

In summary: If you do, then you can use the Pythagorean theorem to find the magnitude of the z-component, since it's just a right triangle in the z-direction. In summary, when given the components of two vectors, C and D, you can find the x, y, and z components of their sum by using the Pythagorean theorem in the x and y directions, and the magnitude of the z-component in the z-direction.
  • #1
JVeazie
1
0

Homework Statement


[/B]
Given the following vector components of vectors C and D:
Cx = 8.10, Cy = -5.40, Cz = -7.90, Dx = 4.40, Dy = -2.50, Dz = 4.50,
find the x, y, z components of their sum.

Homework Equations



No relevant equations that I know of...[/B]

The Attempt at a Solution



I am lost completely. I do understand using (x,y) components, as well as use of the Pythagorean theorem for right triangles, etc...
The z component is throwing me off completely. Do I use the (-) as an indication of direction? Does Z represent a hypotenuse?
Im so confused.
 
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  • #2
JVeazie said:

Homework Statement


[/B]
Given the following vector components of vectors C and D:
Cx = 8.10, Cy = -5.40, Cz = -7.90, Dx = 4.40, Dy = -2.50, Dz = 4.50,
find the x, y, z components of their sum.

Homework Equations



No relevant equations that I know of...[/B]

The Attempt at a Solution



I am lost completely. I do understand using (x,y) components, as well as use of the Pythagorean theorem for right triangles, etc...
The z component is throwing me off completely. Do I use the (-) as an indication of direction? Does Z represent a hypotenuse?
Im so confused.

Z represents that you're working in ##\mathbb{R}^3##, do you know what this means?
 

What is vector addition of components?

Vector addition of components is a mathematical operation that combines two or more vectors to create a resultant vector. It is used to find the overall direction and magnitude of a combined set of forces or displacements.

How is vector addition of components calculated?

Vector addition of components can be calculated using the Pythagorean theorem and trigonometric functions. First, the horizontal and vertical components of each vector are calculated. Then, the components are added together to find the resultant vector’s magnitude and direction.

What is the difference between scalar and vector addition?

Scalar addition involves adding two or more quantities that have only magnitude, such as speed or temperature. Vector addition, on the other hand, takes into account both magnitude and direction of the quantities being added.

What are some real-life applications of vector addition of components?

Vector addition of components is used in various fields such as physics, engineering, and navigation. It is used to calculate the net force on an object, determine the angle and speed of a projectile, and navigate using multiple forces or displacements.

What are some common mistakes when performing vector addition of components?

Some common mistakes when performing vector addition of components include forgetting to convert units, using the wrong trigonometric functions, and forgetting to take into account the direction of the vectors. It is important to pay attention to detail and double check calculations to avoid errors.

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