Cross product of vectors with magnitude 2 and 4 at 60° angle

[Zsmitty3]

One vector with mag 2 pointing East. Other one is mag 4 pointing 30° west of North



Would you use sin or cos and would it be - or +



I did (2*4)cos60°=+4 because they're vectors and we have the A/H sides.

I'm worried about that though because we may use sin? Also Cos is (-) in the II quadrant so it could be negative?

 

[haruspex]

If vectors have magnitude a and b, and the angle between them is C, then is the magnitude of the cross product ab cos C or ab sin C?
What is the angle between the vectors here?
Cross product is not commutative. Changing the order changes the sign. Which sign it takes depends on convention (right hand rule - see http://en.wikipedia.org/wiki/Cross_product).

 

[Zsmitty3]

Okay. So the angle between the two is going to be 60 degrees because the northbound one is going 30 west of N. The other's going east. If the North on was going straight N they would make a 90 degree angle. Since it's 30 degrees west of that (to the left) they're going to make a 60 degree angle. How can you tell the order when it doesn't specify which vector is A and which is B? Also, how do you determine whether it's cos or sin?

 

[cepheid]

Okay. So the angle between the two is going to be 60 degrees because the northbound one is going 30 west of N.

No, 60 degrees is wrong.

The other's going east. If the North on was going straight N they would make a 90 degree angle.

Yes, correct.

Since it's 30 degrees west of that (to the left) they're going to make a 60 degree angle.

Again, no. You combined the 90 degrees with the 30 degrees in the wrong way. Draw a picture. Hint: west and east are opposite directions.

How can you tell the order when it doesn't specify which vector is A and which is B?

This is presumably made clear in your *actual* problem statement, which you did not post.

Also, how do you determine whether it's cos or sin?

For the cross product, only ONE of these is correct, always. Look up the definition of the cross product to see which one.

 

[Zsmitty3]

Ok so I just drew it wrong. It's actually 8sin(120) which gives you the same answer. The 2m vector is listed first so do you just assume it's A?

 

[haruspex]

Ok so I just drew it wrong. It's actually 8sin(120) which gives you the same answer. The 2m vector is listed first so do you just assume it's A?

The angle is 120 measuring anticlockwise from the first vector. The right-hand rule says align RH thumb with first vector, index finger with second vector, and middle finger indicates direction of result. That's towards you, which is the positive direction, so yes it's 8 sin(120^o). Note if the angle had been 210 degrees all of that would still have applied, giving 8 sin(210^o) towards you, i.e. 8 sin(150^o) away from you.