# Proving Vector Orthogonality of b onto a

• darthxepher
In summary, two vectors are orthogonal if they are perpendicular to each other, and to prove this, their dot product must be equal to 0. The formula for calculating the dot product is a · b = |a| * |b| * cos(θ), and yes, two non-zero vectors can be orthogonal. Proving vector orthogonality is related to vector projections because their projections onto each other will be equal to 0 when they are orthogonal.
darthxepher

## Homework Statement

Show that vector orth of b onto a=b-proj of b onto a is orthogonal to a.

I totally don't know where to start :(

and I don't know hat orth of b onto a means...

darthxepher said:
and I don't know hat orth of b onto a means...

Well, that's kind of crucial for answering this question, isn't it. Do you have any lecture notes or textbook in which you can look this up?
Do you remember what the dot product ($\vec a \cdot \vec b$) meant geometrically?

## 1. What does it mean for two vectors to be orthogonal?

Two vectors are orthogonal if they are perpendicular to each other, meaning that the angle between them is 90 degrees.

## 2. How can I prove that two vectors are orthogonal?

To prove that two vectors, a and b, are orthogonal, you must show that their dot product is equal to 0. This means that a dot b = 0.

## 3. What is the formula for calculating the dot product of two vectors?

The dot product of two vectors, a and b, can be calculated using the formula a · b = |a| * |b| * cos(θ), where θ is the angle between the two vectors.

## 4. Can two non-zero vectors ever be orthogonal?

Yes, two non-zero vectors can be orthogonal if their dot product is equal to 0. This can occur if the angle between the vectors is 90 degrees.

## 5. How does proving vector orthogonality relate to vector projections?

Proving vector orthogonality is related to vector projections because when two vectors are orthogonal, their projections onto each other will be equal to 0. This can be seen in the formula for the projection of vector b onto vector a, which is given by proja(b) = (a · b)/|a|.

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