Finding the angle between vectors a and m, knowing the magnitude of m and n

In summary, the problem is to find the angle between vectors a and m, given the magnitude of m and n, as well as the angle between m and n (which is 60 degrees). Using the formula for finding the angle between two vectors, it appears that the angle is 30 degrees. However, the given answer is 54.7 degrees. It is unclear how this result was obtained, as it may not be correct. Further clarification is needed to determine the correct angle.
  • #1
piesand
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Summary: Finding angle between vectors a and m, knowing magnitude of m and n, also the angle between m and n with 60 degrees.

Screen Shot 2019-11-14 at 10.36.49 AM.png


Using geometry, it looks like the angle is 30 degrees but the answer is suppose to be 54.7 degrees. I'm not sure how to solve this.
 
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  • #2
Hint:
$$\cos \theta= \frac {\vec a . \vec m}{||\vec a|| ||\vec m||}$$
 
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piesand said:
Summary: Finding angle between vectors a and m, knowing magnitude of m and n, also the angle between m and n with 60 degrees.

View attachment 252831

Using geometry, it looks like the angle is 30 degrees but the answer is suppose to be 54.7 degrees. I'm not sure how to solve this.
Sometimes the given answer is not true. Show, please, how did you get your result. It might be correct 😉
 
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FAQ: Finding the angle between vectors a and m, knowing the magnitude of m and n

1. How do I find the angle between two vectors if I know the magnitude of both vectors?

To find the angle between two vectors, you can use the dot product formula: cos(theta) = (a*m)/(|a||m|), where a and m are the two vectors and |a| and |m| are their magnitudes. The angle between the two vectors can then be found by taking the inverse cosine of the resulting value.

2. Can I find the angle between two vectors if I only know the magnitude of one vector?

Yes, you can still find the angle between two vectors if you only know the magnitude of one vector. You will need to use the Pythagorean theorem to find the missing component of the vector, and then use the dot product formula mentioned above to find the angle.

3. Is there a specific unit for measuring the angle between vectors?

The angle between vectors is usually measured in radians or degrees. Radians are the standard unit for measuring angles in mathematics, while degrees are more commonly used in everyday life. Make sure to use the same unit for both vectors when finding the angle between them.

4. Can I use the magnitude of the vectors to determine if they are parallel or perpendicular?

Yes, the magnitude of two vectors can help determine if they are parallel or perpendicular. If the magnitude of two vectors are equal, they are parallel. If the dot product of the two vectors is zero, they are perpendicular.

5. Is it possible to find the angle between more than two vectors?

Yes, it is possible to find the angle between more than two vectors. However, the dot product formula mentioned above only works for finding the angle between two vectors. To find the angle between multiple vectors, you will need to use trigonometric functions or more advanced mathematical techniques.

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