Chilly vectors

The most convenient way to express vectors in the two dimensional plane is in the familiar (x,y) Cartesian coordinates. However, one can express vectors in other coordinate systems as well. For example, another useful coordinate system for the plane is polar coordinates (r, θ \theta ), where r is the distance from the origin and θ \theta is the angle counterclockwise from the positive horizontal axis. Consider the vector v \vec{v} with components ( 0 , 1 ) (0,1) in polar coordinates. Unlike the ( 0 , 1 ) (0,1) vector in Cartesian coordinates the direction of v \vec{v} changes depending on the angular coordinate of the point at which the vector is at. This is due to the fact that there is a 1 1 in the θ \theta direction. Since the vector has no radial component, it always is tangent to the circle (points in the direction of increasing angle). For what value of θ \theta in degrees is v \vec{v} parallel to the positive direction along the x-axis?


The answer is 270.

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1 solution

David Mattingly Staff
May 13, 2014

The vector ( 0 , 1 ) (0,1) always points in the positive θ \theta direction and has no radial component. Therefore it is always parallel to the "counterclockwise" tangent to a circle. This tangent points parallel to the positive x-axis when θ = 270 \theta=270 degrees.

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