Vector Projection Homework: Figuring Out the Angle

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To project vector A onto the x and y axes, determine the angle it makes with line C, which is parallel to the x-axis. Since vector A is perpendicular to vector B and forms a right triangle with line C, the angle A makes with C is the complement of 30 degrees, resulting in a 60-degree angle. This angle is also the same when extended to the x-axis due to corresponding angles in parallel lines. Therefore, the angle used for the projection of vector A onto the axes is 60 degrees. Understanding these relationships is crucial for accurately performing vector projections.
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Homework Statement



I have a vector diagram attached below. Vector A is perpendicular to vector B.

How do you figure out what angle to use in order to project vector A onto the x and y axis?


Homework Equations



A dot B = ABcos(angle)

The Attempt at a Solution



180-30-90 = 60?
 

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Exactly right- though you don't really need the "180" and "90". Extend A back to line C and you will see that the three lines form a right triangle. That tells you that the angle A makes with C is the complement of 30 degeres, 60. And, since C is parallel with the x-axis, extending it further shows (corresponding angles in parallel lines) that it makes the same angle with the x-axis.
 

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