Is the vector parallel to the plane?

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SUMMARY

In the discussion, it is established that if a plane contains the line represented by the equation $\overrightarrow{v}_1=\overrightarrow{a}+t\overrightarrow{u}$, then the vector $\overrightarrow{u}$ is indeed parallel to the plane. This conclusion is reached through the understanding of vector and plane relationships in three-dimensional space. The confirmation of this relationship is acknowledged by multiple participants in the discussion.

PREREQUISITES
  • Understanding of vector equations in three-dimensional space
  • Knowledge of plane geometry and its properties
  • Familiarity with the concept of parallel vectors
  • Basic algebraic manipulation of vector equations
NEXT STEPS
  • Study the properties of vector lines and planes in 3D geometry
  • Learn about vector projections and their applications
  • Explore the implications of vector parallelism in physics and engineering
  • Investigate the use of vector equations in computer graphics
USEFUL FOR

Students of mathematics, physics enthusiasts, and professionals in engineering or computer graphics who seek to understand the relationship between vectors and planes.

mathmari
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Hello! :o

When a plane contains the line $\overrightarrow{v}_1=\overrightarrow{a}+t\overrightarrow{u}$, does this mean that the vector $\overrightarrow{u}$ is parallel to the plane?? (Wondering)
 
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mathmari said:
Hello! :o

When a plane contains the line $\overrightarrow{v}_1=\overrightarrow{a}+t\overrightarrow{u}$, does this mean that the vector $\overrightarrow{u}$ is parallel to the plane?? (Wondering)

Yes
 
Prove It said:
Yes

Ok... Thank you! (Smile)
 

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