What did I do wrong with these vectors?

• Newphysicsguy
In summary, the conversation discusses finding the sum of two vectors, a and b, and the steps involved in the calculation. The final answer is given as a vector with components 4.0 and 0.1, although there may be a typo in the book with the component 4.1 instead of 4.01. The conversation also highlights the importance of double-checking calculations to ensure accuracy.
Newphysicsguy
Find $\vec{a}+\vec{b}$ (Look at the picture)

The book shows the solutions as :
a. 4.1m Along the +x axis.

I however do not know where I went wrong in my calculations.

$\vec{a}+\vec{b}=\begin{bmatrix} a_x+b_x\\ a_y+b_y \end{bmatrix}=\begin{bmatrix} |\vec{a}|\cos(30)+|\vec{b}|\cos(45)\\ |\vec{a}|\sin(30)-|\vec{b}|\sin(45) \end{bmatrix}=\begin{bmatrix} \frac{3\sqrt{3}}{2}+\sqrt{2}\\ 1.5-\sqrt{2} \end{bmatrix}=\begin{bmatrix} 4.01\\ .085 \end{bmatrix}$NOTE: If I posted this is the wrong location I am sorry. This is not homework, I am doing it on my own time.
EDIT: thank you for moving my post to the correct location.

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Check your calculation for $a_y$.

That was a typo, it should be 3sin(30) which comes to be 1.5 which I had in the 3rd step. Sorry for the typo. Unless I did it wrong anyways? Either way $a_y$ does not effect $a_x+b_x$ which is also off from what the book says.

You're right, your numbers in the next to last step are OK. I noticed it while you were writing your latest post. As far as I can tell, your answer is OK. Whoever wrote the answer you were given, didn't round it off correctly or consistently. To one decimal place, the components should be 4.0 and 0.1. To zero decimal places, they should be 4 and 0.

It's probably a typo for 4.01 instead of 4.1. Those things do happen. I've seen it lots of times.

Thank you. I am never sure if I am wrong or if the book is wrong. It's better to always assume I am wrong.

1. What are vectors and why are they important in science?

Vectors are mathematical quantities that have both magnitude and direction. They are important in science because they are used to represent physical quantities such as velocity, acceleration, and force. They also play a crucial role in analyzing and solving problems in various fields of science, including physics, engineering, and computer science.

2. How do I know if I have made a mistake with my vectors?

If your vector calculations do not produce expected results or do not follow the laws of vector algebra, it is likely that you have made a mistake. Double-check your calculations and make sure you have correctly represented the magnitude and direction of each vector.

3. What are some common errors when working with vectors?

Some common errors when working with vectors include: forgetting to account for the direction of a vector, mixing up the order of vector components, using the wrong mathematical operations, and forgetting to convert between units when necessary.

4. How can I avoid making mistakes with vectors?

To avoid making mistakes with vectors, it is important to have a solid understanding of vector concepts and laws of vector algebra. Double-check your calculations and make sure you have correctly represented the magnitude and direction of each vector. It is also helpful to use diagrams or visual aids to represent vectors and their relationships.

5. What resources can I use to improve my understanding of vectors?

There are many resources available to help you improve your understanding of vectors, including textbooks, online tutorials, and practice problems. You can also seek help from a teacher, tutor, or fellow scientist who is knowledgeable in the subject. Additionally, experimenting with and visualizing vectors in real-world scenarios can also enhance your understanding of their applications.

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