# Cross product or vector product.

What does the angle theta acutally means in cross product because I have seen in many places it is written that theta is the angle at which two vector on a given plane will coinside with each other so that there will be only one direction. Is it true and why they defined it in this way , I need more information on this

fresh_42
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2021 Award
What does the angle theta acutally means in cross product because I have seen in many places it is written that theta is the angle at which two vector on a given plane will coinside with each other so that there will be only one direction. Is it true and why they defined it in this way , I need more information on this
Have you read this: https://en.wikipedia.org/wiki/Cross_product#Geometric_meaning ?

If there are two vector in a given plane and they are not connected tail to tail then what we have to doo. I think now we have to connect the two vectors tail to tail by the smallest angle theta so that we can have a vector perpendicular to both the vectors. Correct me if I am wrong

fresh_42
Mentor
2021 Award
If there are two vector in a given plane and they are not connected tail to tail then what we have to doo. I think now we have to connect the two vectors tail to tail by the smallest angle theta so that we can have a vector perpendicular to both the vectors. Correct me if I am wrong
A vector is a direction and a length. Where you "connect" them depends on what you want to do.
E.g. a force has a direction and an amount. Whether you can use it to pull the chair depends on where you apply the force.
I think you're on the right track. Cancel the word "smallest" and it looks ok. The angle is defined by the directions the vectors point. There is no smallest or biggest. Of course you have to put them tail to tail to determine the angle between them.

• prashant singh
robphy
Homework Helper
Gold Member
In the cross-product, the first goal should be to determine the signed-area of the parallelogram formed by the vectors.
Slide the vectors to have their tails meet, then measure the angle from the first vector to the second vector.
Then you'll take the sine of that angle.
In three dimensions, if this area is nonzero,
there will be a unique line that is perpendicular to that parallelogram.

Thanks brooo , cooool
In the cross-product, the first goal should be to determine the signed-area of the parallelogram formed by the vectors.
Slide the vectors to have their tails meet, then measure the angle from the first vector to the second vector.
Then you'll take the sine of that angle.
In three dimensions, if this area is nonzero,
there will be a unique line that is perpendicular to that parallelogram.