Finding Parallel and Orthogonal Vectors for u and v

In summary, the task is to find two vectors, u1 and u2, given two initial vectors, u and v. u1 must be parallel to v and u2 must be orthogonal to v. The equation u = u1 + u2 is also given. The person asking for help is unsure how to approach the problem and asks for clarification and hints. They mention that their book only talks about determining orthogonality through the dot product and they are not familiar with determining parallel vectors. They also suggest drawing a diagram to aid in understanding the problem.
  • #1
Whiz
20
0

Homework Statement



For u=(26, 6, 21) and v=(−27, −9, −18) , find the vectors u1 and u2 such that:

(i) u1 is parallel to v

(ii) u2 is orthogonal to v

(iii) u = u1 + u2


Homework Equations



None

The Attempt at a Solution



I'm quite lost on this question and not sure how to even start. Can someone explain the question and give me some hints to get started?

Thanks in advance.
 
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  • #2
Are you sure that there are no relevant equations? What about those defining defining parallel and orthogonal?
 
  • #3
Drawing a diagram is always great.
 
  • #4
There aren't any other questions or equations about this. All I know is if their dot product is 0, then its orthogonal, and my book doesn't even mention parallel.
 

FAQ: Finding Parallel and Orthogonal Vectors for u and v

What is the difference between parallel and orthogonal?

Parallel refers to two or more lines, planes, or objects that never intersect and always maintain the same distance from each other. Orthogonal, on the other hand, refers to two or more lines, planes, or objects that intersect at a right angle.

How are parallel and orthogonal concepts used in math and science?

In math and science, parallel and orthogonal concepts are used to describe relationships between lines, planes, or objects. They are also used in geometry and trigonometry to calculate angles and distances.

What is an example of parallel lines in real life?

An example of parallel lines in real life is railroad tracks. They always maintain the same distance from each other and never intersect.

What is an example of orthogonal planes in architecture?

An example of orthogonal planes in architecture is a building with rectangular walls. The walls intersect at right angles, creating a stable and sturdy structure.

How are parallel and orthogonal used in computer science?

In computer science, parallel and orthogonal concepts are used in programming to describe algorithms and data structures. They are also used in computer graphics to create 3D objects and scenes.

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