Calculate the Resultant Vector of 3D Vectors

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Homework Help Overview

The discussion revolves around calculating the resultant vector from three given three-dimensional vectors, including their components in the x, y, and z directions. The original poster expresses difficulty in determining the resultant vector's magnitude after summing the components.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the calculation of the resultant vector's components and the subsequent challenge of finding its magnitude. There is mention of using the Pythagorean theorem for two-dimensional vectors, with questions about extending this method to three dimensions.

Discussion Status

Some participants have provided guidance on applying the Pythagorean theorem to find the magnitude of the resultant vector, suggesting a method to incorporate the z-component. However, there is no explicit consensus on the overall approach, and multiple interpretations of the problem are being explored.

Contextual Notes

The original poster's calculations of the resultant vector components are noted, but there is uncertainty regarding the next steps to find the magnitude. The discussion reflects a lack of complete information on how to integrate the third dimension into the calculations.

chemguy990
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Homework Statement



I am having a tough time finding the resultant vector of the the following three dimensional vector:

d1x=2.33 cm, d1y= 3.84 cm, d1z= -1.2cm
d2x=3.41 cm, d2y= -1.01 cm, d2z = -3.29 cm
d3x= -1.04 cm, d3y= 1.93 cm, d3z = 0 cm

Find the resultant vector magnitude.

Homework Equations





The Attempt at a Solution



I have added the vector components and got the following:
rx= 4.7, ry= 4.76, rz= -4.49

Not sure where to go next.
 
Last edited:
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So you have calculated the sum of the three vectors (the resultant vector). Now how do you get its magnitude?
 
I know using the pythagorean theorem will get the resultant for xy plane vectors...not sure how to get the third plane calculations.
 
chemguy990 said:
I know using the pythagorean theorem will get the resultant for xy plane vectors...not sure how to get the third plane calculations.

You'd apply pythagorean a second time, using the z-vector and the xy plane vector... draw a picture if you are unsure...

so the magnitude of the resultant is just \sqrt{r_x^2 +r_y^2 + r_z^2}