Vector in 3d with given by magnitude and angle

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SUMMARY

The discussion focuses on determining the component form of a vector \( v \) that lies in the yz-plane with a magnitude of 2 and an angle of 30 degrees with the positive y-axis. The x-component of the vector is confirmed to be zero, leading to the representation \( <0, v_1, v_2> \). The components can be calculated using trigonometric functions, specifically sine and cosine, to find \( v_1 \) and \( v_2 \).

PREREQUISITES
  • Understanding of vector representation in component form
  • Knowledge of trigonometric functions: sine and cosine
  • Familiarity with angles in standard position
  • Basic concepts of the Cartesian coordinate system
NEXT STEPS
  • Learn how to calculate vector components using trigonometric identities
  • Explore vector operations such as addition and subtraction in 3D
  • Study the properties of vectors in different planes, particularly the yz-plane
  • Investigate applications of vectors in physics, such as force and motion
USEFUL FOR

Students studying physics or mathematics, educators teaching vector analysis, and anyone interested in understanding vector components in three-dimensional space.

cbarker1
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MHB
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Dear everyone,Direction Write the vector in component form.

v lies in the yz planeplane, has magnitude 2, and makes an angle of 30 degrees with the positive y axis.

Work
I know that the x component is zero.
<0,v1,v2​>

Thanks
Cbarker1
 
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