- #1
darthxepher
- 56
- 0
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...
Two vectors are orthogonal if they are perpendicular to each other, meaning that the angle between them is 90 degrees.
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.
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.
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.
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 proj_{a}(b) = (a · b)/|a|.