Components and Vectors and Lengths, Oh My

[Aquas]

Hey guys! I am back for a second time. (Woo) More Awesome Physics underway!

Homework Statement

The components of a vector V are often written (Vx, Vy, Vz). What are the components and length of a vector which is the sum of the two vectors, V1 and V2, whose components are (3.4, 1.0, 15.0) and (5.1, -4.6, -1.0)?

Homework Equations

(Vx)=8.5
(Vy)=-3.6
(Vz)=14

The Attempt at a Solution

To my understanding it should be (Vx)² + (Vy)² + (Vz)² = √Length

But my Program say nay to such an answer...Is there somthing I missed?

 

[Aquas]

Ugh I fail, a Negative Being Squared is Positive... Void all that, I suck. : (

 

[tomcue]

Hi there! It's great to see your enthusiasm for physics. Let's take a closer look at the components and length of a vector. First, the components of a vector are the values that make up the vector in terms of its direction and magnitude in each dimension. In this case, the components of V1 are 3.4 in the x-direction, 1.0 in the y-direction, and 15.0 in the z-direction. Similarly, the components of V2 are 5.1 in the x-direction, -4.6 in the y-direction, and -1.0 in the z-direction.

To find the components and length of the vector V1+V2, we can add the corresponding components of V1 and V2. So, in the x-direction, we have 3.4 + 5.1 = 8.5. In the y-direction, we have 1.0 + (-4.6) = -3.6. And in the z-direction, we have 15.0 + (-1.0) = 14.0. Therefore, the components of V1+V2 are (8.5, -3.6, 14.0).

As for the length of the vector V1+V2, you are on the right track with the equation (Vx)² + (Vy)² + (Vz)² = √Length. However, you need to square each component and then take the square root of the sum. So, the length would be √(8.5² + (-3.6)² + 14.0²) = 16.6.

I hope this clears things up for you. Keep up the good work!