Vector Projection Homework: Figuring Out the Angle

[iflabs]

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?

 

[HallsofIvy]

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.

 

[Architeuthis Dux]

I would approach this problem by first identifying the given information and the goal of the problem. From the diagram, it is clear that vector A is perpendicular to vector B. The goal is to find the angle needed to project vector A onto the x and y axis.

To solve this problem, I would use the dot product formula, which relates the angle between two vectors to their magnitudes. In this case, the formula would be A dot B = ABcos(angle).

Since vector A is perpendicular to vector B, the dot product would be equal to 0, as the cosine of 90 degrees is 0. This means that the angle between vector A and B is 90 degrees.

To project vector A onto the x and y axis, we need to find the angle between vector A and the x and y axis. Since vector A is perpendicular to vector B, it is also perpendicular to the x axis. This means that the angle between vector A and the x axis is also 90 degrees.

To find the angle between vector A and the y axis, we can use basic trigonometry. Since vector A and B form a right triangle, we can use the Pythagorean theorem to find the magnitude of vector A. Once we have the magnitude, we can use the inverse tangent function to find the angle between vector A and the y axis.

In conclusion, the angle needed to project vector A onto the x and y axis is 90 degrees for the x axis and the inverse tangent of the magnitude of vector A divided by the magnitude of vector B for the y axis.