Angle between Two Vectors
Figure 1 shows two vectors in standard position.
The angle between two vectors in standard position can be calculated as follows:
ANGLE BETWEEN TWO VECTORS:
If θ is the angle between two non-zero vectors in standard position u and v:
Where and
Let's look at some examples.
Step 1: Find the dot product of the vectors. Remember the result will be a scalar.
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Step 2: Find the magnitudes of each vector.
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||u|| = ||u|| = ||u|| = ______________________________ ||v|| = ||v|| = ||v|| = |
Step 3: Substitute and solve for θ.
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Step 1: Find the dot product of the vectors. Remember the result will be a scalar.
|
|
Step 2: Find the magnitudes of each vector.
|
||u|| = ||u|| = ||u|| = ______________________________ ||v|| = ||v|| = ||v|| = |
Step 3: Substitute and solve for θ.
As soon as you determine that the dot product is 0 you do not need to calculate the magnitudes. They are completed here for your benefit. Note that when two vectors in standard position have a dot product of 0 the angle between them is 90°. |
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Related Links: Math algebra Decomposing a Vector into Components The First Derivative Rule Pre Calculus |
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