Vectors Parallel and Perpendicular

In summary, the conversation is about representing vector w as the sum of two vectors, one parallel to vector v and one perpendicular to vector v. The use of the dot product is also mentioned. The person is unsure of where to begin and asks for help in finding the general form of vectors parallel and perpendicular to v. They are also asked to find a vector perpendicular to v.
  • #1
chodge17
2
0

Homework Statement




Let vector v=<1,-2, 6> and vector w=<30,-11, -2>. Represent vector w in the form of

w=g+h, where g is parallel to v and h is perpendicular to v. Using the dot product


Homework Equations





The Attempt at a Solution


I don't even know where to begin. I think you maybe do v*w first but I don't know.
 
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  • #2
Do you know the general form of vectors parallel to v? Do you know the general form of vectors perpendicular to v?
 
  • #3
In most cases, yes. But in this instant, I don't know where to begin. What throws me off is the w=g+h. I know what the question is asking I just don't know how it is asking it. The question is wanting me to find vector g< , , , > and vector h< , , , >
 
  • #4
Can you give me a vector perpendicular to v?
 

FAQ: Vectors Parallel and Perpendicular

1. What is the definition of parallel vectors?

Parallel vectors are two or more vectors that have the same direction or are co-linear. This means that they are either pointing in the same direction or in exactly opposite directions.

2. How can you determine if two vectors are parallel?

To determine if two vectors are parallel, you can use the dot product formula. If the dot product of two vectors is equal to the product of their magnitudes, then they are parallel. Alternatively, you can also compare the direction and magnitude of the two vectors visually.

3. What are perpendicular vectors?

Perpendicular vectors are two or more vectors that intersect at a right angle (90 degrees). This means that their dot product is equal to zero.

4. How can you determine if two vectors are perpendicular?

To determine if two vectors are perpendicular, you can use the dot product formula. If the dot product of two vectors is equal to zero, then they are perpendicular. Alternatively, you can also compare the direction and magnitude of the two vectors visually.

5. Can parallel vectors also be perpendicular?

No, parallel vectors cannot be perpendicular. If two vectors are parallel, their dot product will not be equal to zero, which is a necessary condition for perpendicular vectors. Therefore, parallel vectors cannot be perpendicular.

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