The Dot Product and Cross Product: Finding the Angle Between Two Vectors

[raptik]

Homework Statement

If theta is the angle between two non-zero vectors A and B, then which of the following angles theta results in A dot B = |A x B|?

Homework Equations

A dot B = ABcos(theta)
A x B = ABsin(theta)

The Attempt at a Solution

There were two choices in the multiple choice answers where cos(theta) = |sin(theta)|

1 is 225 degrees and the other is 315 degrees. The correct answer is 315 degrees. Can somebody explain or help illustrate why 225 is wrong and 315 is right?

 

[newguy1234]

When performing the dot and cross product the angle used in the formulas you listed is always the smaller angle between the two vectors. So an angle of 315 degrees corresponds to an angle of 45 degrees (360-315=45). And 225 corresponds to an angle of 135 degrees. This should help you answer your question.

 

[newguy1234]

Additionally the Magnitude of the cross product is defined as:

|A x B|= |A||B| sin(theta)

not = |AB sin(theta)| or AB |sin(theta)| as you eluded to in your post.

 

[Redbelly98]

Additionally the Magnitude of the cross product is defined as:

|A x B|= |A||B| sin(theta)

not = |AB sin(theta)| or AB |sin(theta)| as you eluded to in your post.

True as long as we agree that 0° ≤ θ ≤ 180°, as is common practice. But apparently the question's author has a different idea about the angle between two vectors!