How do you find the magnitude of vectors?

[deaninator]

Homework Statement

Consider the two vectors r1 and r2 shown in the diagram. The magnitudes of the two vectors are: r1=6.1 and r2=9.3. The vectors directions relative to the x-axis are defined by the angles: θ1=25 degrees and θ2=51 degrees

What is the magnitude of the vector R=r1+r2?
A = 15.0226
But how do I get that answer?

Homework Equations

*Please refer to picture*
https://www.physicsforums.com/attachment.php?attachmentid=29294&d=1287716259

The Attempt at a Solution

Homework Statement

Homework Equations

The Attempt at a Solution

 

[cepheid]

Resolve the vectors into x and y-components using the angles and trigonometry. Then add up the x-components of the individual vectors to get the x-component of the resultant. Same for the y-components. Once you have the x and y components of the resultant, you can use Pythagoras to get the total magnitude:

R_x = r_1x + r_2x

R_y = r_1y + r_2y

R² = R_x² + R_y² (Pythagorean theorem)

OR instead of doing it using x and y-components, you could just determine the magnitude directly from the triangle in your diagram, and the cosine law.

 

[deaninator]

Resolve the vectors into x and y-components using the angles and trigonometry. Then add up the x-components of the individual vectors to get the x-component of the resultant. Same for the y-components. Once you have the x and y components of the resultant, you can use Pythagoras to get the total magnitude:

R_x = r_1x + r_2x

R_y = r_1y + r_2y

R² = R_x² + R_y² (Pythagorean theorem)

OR instead of doing it using x and y-components, you could just determine the magnitude directly from the triangle in your diagram, and the cosine law.

Do you always use the cosine law?

 

[cepheid]

Do you always use the cosine law?

I don't really know what you're asking. I mean, I just showed you a method of doing it that did not involve the cosine law (the first method). But, whenever the cosine law is applicable, then you can use it.

 

[rwisz]

To find the magnitude of a vector, you can use the Pythagorean theorem. The magnitude of a vector is the square root of the sum of the squares of its components. In this case, the components of the vector R are r1 and r2, so the magnitude of R can be found using the formula:

|R| = √(r1^2 + r2^2)

Substituting the values given in the problem, we get:

|R| = √(6.1^2 + 9.3^2) = √(37.21 + 86.49) = √123.7 = 11.11

Therefore, the magnitude of vector R is approximately 11.11.