Two vectors A and B have magnitude A = 3.00 and B = 3.00. Their vector product is A x B= -5.00k + 2.00i. What is the angle between A and B?
According to the answer, the angle is 37 degrees. I see where this comes from. However, we know that sin(36,75)=sin(143,25)
So the magnitude of vector C, where vector C is the cross product of vectors A and B is
3*3sin(36,75)=3*3sin(143,25)=5,385
My question is:
Why is 37 degrees the only correct answer if 143 degrees also works?
Thanks for help
AxB has to form a right-handed system. If angles greater than 90 degrees are involved, that does not hold.
The angle between two vectors can actually have multiple solutions. In this case, both 37 degrees and 143 degrees are valid angles between vectors A and B.
The reason why 37 degrees is typically considered the "correct" answer is because of the convention used for measuring angles between vectors. In mathematics and physics, the angle between two vectors is usually measured within the range of 0 to 180 degrees.
When working with the cross product of two vectors, the magnitude of the resulting vector is given by the formula |C| = |A| |B| sin(theta), where |A| and |B| are the magnitudes of vectors A and B, and theta is the angle between them. In this case, |A| = 3.00 and |B| = 3.00, and the magnitude of the cross product vector C is 5.385.
Now, the sin function has a periodicity of 360 degrees, meaning that sin(theta) = sin(theta + n * 360), where n is an integer. This means that both 37 degrees and 143 degrees satisfy the equation sin(theta) = 5.385 / (3.00 * 3.00).
However, when measuring the angle between vectors, we typically consider only the acute (smaller) angle between them. This convention is followed to maintain consistency and to simplify calculations. Therefore, in this case, the angle of 37 degrees is considered the "correct" answer because it is the smaller angle between vectors A and B.