Magnitude of the vector r=r2−r1?

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SUMMARY

The discussion focuses on calculating the magnitude of the vector r, defined as r = r2 - r1, where r1 and r2 are two vectors with magnitudes of 5.9 and 8.5, respectively. The angles of these vectors relative to the x-axis are θ1 = 37 degrees and θ2 = 65 degrees. Participants break down the vectors into their x and y components using trigonometric functions, specifically sine and tangent, to facilitate the calculation of the resultant vector's components. The challenge lies in correctly applying the component subtraction to find the magnitude and angle of vector r.

PREREQUISITES
  • Understanding of vector components and trigonometric functions (sine, cosine, tangent)
  • Familiarity with vector subtraction and resultant vectors
  • Basic knowledge of angles in standard position
  • Ability to perform calculations involving degrees and vector magnitudes
NEXT STEPS
  • Calculate the x and y components of r1 and r2 using the formulas: x1 = r1 * cos(θ1), y1 = r1 * sin(θ1), x2 = r2 * cos(θ2), y2 = r2 * sin(θ2)
  • Perform the vector subtraction to find the components of vector r: r_x = x2 - x1, r_y = y2 - y1
  • Use the Pythagorean theorem to find the magnitude of vector r: |r| = √(r_x² + r_y²)
  • Determine the angle of vector r with respect to the x-axis using the arctangent function: θ_r = tan⁻¹(r_y / r_x)
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Students studying physics or mathematics, particularly those focusing on vector analysis and trigonometry, as well as educators seeking to clarify vector component calculations.

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Homework Statement



Consider the two vectors r1 and r2 . The magnitudes of the two vectors are: r1=5.9 and r2=8.5. The vectors directions relative to the x-axis are defined by the angles: θ1=37 degrees and θ2=65 degrees.

What is the magnitude of the vector r=r2−r1?

What is the angle between r and the x axis? (in degrees)

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Homework Equations


Break each vector into components: x1, y1, x2, y2, then consider the vector r as (x2-x1,y2-y1)

The Attempt at a Solution



Break each vector into components: x1, y1, x2, y2, then consider the vector r as (x2-x1,y2-y1)

So broke each vector into triangles and calculated the x-component & y= components:
R1 x component: tan37deg=3.55/x= 4.73 N
R1 y component: sin37deg= y1/5.9=3.55 N
R2 x component: tan65=7.7/x=3.59
R2 y component: sin65=y2/8.5

then i got stuck here... help me out please?
 
Last edited:
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Now that you have x1, y1, x2, and y2, why can't you write the vector as (x2-x1,y2-y1)?
 

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