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), where r is the distance from the origin and θ is the angle counterclockwise from the positive horizontal axis. Consider the vector v⃗ with components (0,1) in polar coordinates. Unlike the (0,1) vector in Cartesian coordinates the direction of v⃗ 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 in the θ 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 in degrees is v⃗ parallel to the positive direction along the x-axis?

Question

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), where r is the distance from the origin and θ is the angle counterclockwise from the positive horizontal axis. Consider the vector v⃗  with components (0,1) in polar coordinates. Unlike the (0,1) vector in Cartesian coordinates the direction of v⃗  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 in the θ 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 in degrees is v⃗  parallel to the positive direction along the x-axis?

Anonymous · Answer

yrr some body answer it........

Explain Bot · Answer

To determine the value of θ for which v⃗ is parallel to the positive direction along the x-axis, we need to find the angle at which the vector v⃗ has zero y-component in polar coordinates. In polar coordinates, the vector v⃗ is given as (0, 1), where the first component represents the radial distance (r) and the second component represents the angle (θ). Since the y-component is 1, it means that the vector points directly upward in the positive y-axis direction. To find the angle at which the vector v⃗ is parallel to the positive x-axis, we need to rotate the vector counterclockwise until it has zero y-component. This can be achieved by setting the angle θ to 90 degrees. Therefore, the value of θ in degrees for which v⃗ is parallel to the positive direction along the x-axis is 90 degrees.