The question is...
"If A cross product B = the vector C, calculate the angle alpha between the vectors A and C and the angle beta between the vectors B and C."
I think I have the answer but not sure and I know this will be a test question so can I get some help? Thank you.
"If A cross product B = the vector C, calculate the angle alpha between the vectors A and C and the angle beta between the vectors B and C."
I think I have the answer but not sure and I know this will be a test question so can I get some help? Thank you.
-
The angle is 90 degrees, for both cases and this is because of the definition of the cross product. What happens is the end result vector is perpendicular to both crossed vectors.
In other words, since a x b = c, the vector c is perpendicular to both b and to a as well.
Simple example: take a = <1, 0, 0> and b = <0, 1, 0>. a x b = c = <0, 0, 1>
a dot c = 0 and b dot c = 0, the only time dot product is 0 is for vectors whose angle between them is 90 degrees.
Hope this helps.
In other words, since a x b = c, the vector c is perpendicular to both b and to a as well.
Simple example: take a = <1, 0, 0> and b = <0, 1, 0>. a x b = c = <0, 0, 1>
a dot c = 0 and b dot c = 0, the only time dot product is 0 is for vectors whose angle between them is 90 degrees.
Hope this helps.