Finding the z component of vectors that form a triangle?

In summary, the conversation discusses how to calculate the z component of a cross product between two vectors with given magnitudes and angles. It is important to consider direction when determining the correct answer.
  • #1
rockchalk1312
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0
For the vectors in the figure, with a = 1.1 and b = 2.6, what are (a) the z component of a x b, (b) the z component of a x c, and (c) the z component of b x c?


Everything I've tried to look up involves vectors that are in unit notation, etc. I just don't understand how to do it when all you have for the vector is one number.
 

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  • #2
With the information given, you can work out the angle between a and c.
Then use the formula for the cross product which uses the magnitudes and angle.
 
  • #3
ap123 said:
With the information given, you can work out the angle between a and c.
Then use the formula for the cross product which uses the magnitudes and angle.

So using a x b = |a| |b| sinθ told me that the z component of a x b = (1.1)(2.6)sin90 = 2.9.

And for b x c = (2.6)(2.823)sin(90-67.07)=2.9.

These were both correct, but then when I tried to do a x c = (1.1)(2.823)sin67.06 = 2.9 this was the wrong answer.

Am I missing something completely obvious?

Thank you for your help!
 
  • #4
rockchalk1312 said:
So using a x b = |a| |b| sinθ
That should be |a x b| = |a| |b| sinθ. If you want a x b, not just its magnitude, you need to worry about direction. Yes, it's in the z direction, but is it positive or negative? You need to apply the convention for a x b (as distinct from b x a) to determine that.
From the diagram, you have a + b + c = 0. So 0 = a x (a + b + c) = a x a + a x b + a x c = a x b + a x c. It follows that a x b and a x c must have opposite signs.
 
  • #5
haruspex said:
Yes, it's in the z direction, but is it positive or negative?

Perfect THANK you that was certainly what I was missing.
 

Related to Finding the z component of vectors that form a triangle?

1. What is the z component of a vector?

The z component of a vector is the measure of its magnitude in the z direction, or the vertical direction, on a 3D coordinate system.

2. How do you find the z component of a vector?

To find the z component of a vector, you can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse would be the magnitude of the vector, and the other two sides would be the x and y components of the vector. Then, you can use simple trigonometry to solve for the z component.

3. Can you find the z component of a vector if you only have the magnitude and the angle?

Yes, you can find the z component of a vector if you have the magnitude and the angle. Using the magnitude as the hypotenuse and the angle as one of the angles of a right triangle, you can use trigonometry to solve for the other sides of the triangle, which would be the x and y components. Then, you can use the Pythagorean theorem to find the z component.

4. How do you find the z component of vectors that form a triangle?

To find the z component of vectors that form a triangle, you can use the law of cosines, which states that the square of one side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of those two sides and the cosine of the included angle. By applying this law to each side of the triangle, you can solve for the z components of each vector.

5. Why is finding the z component of vectors that form a triangle important?

Finding the z component of vectors that form a triangle is important because it allows us to accurately represent and analyze 3D objects and movements. It also helps us to solve problems and make predictions in various fields such as physics, engineering, and computer graphics.

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