Math Assignment Help With Direction of Vectors

2.3: Direction of Vectors:

The direction of a vector is often expressed as an angle of rotation of the vector about its "tail" from east, west, north, or south. For example, a vector can be said to have a direction of 30 degrees North of West that means, a vector pointing west has been rotated through 30 degrees towards the north direction, of 65 degrees East of South which means a vector pointing South has been rotated 65 degrees towards the east direction.

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The direction of a vector is often expressed as a counterclockwise angle of rotation of the vector about its "tail" from due East. Using this convention, a vector with a direction of 30 degrees is a vector which has been rotated 30 degrees in a counterclockwise direction relative to due east. A vector with a direction of 160 degrees is a vector which has been rotated 160 degrees in a counterclockwise direction relative to due east. A vector with a direction of 270 degrees is a vector which has been rotated 270 degrees in a counterclockwise direction relative to due east. This is one of the most common conventions for the direction of a vector and will be utilized throughout this unit.

direction of vectors

30o counter-clockwise rotations from east.

vector

240o

counter clockwise rotations from east

240o counter-clockwise rotations from east

Vectors in multiple-dimension coordinate systems can be split up into their component vectors. In the two-dimensional case, this results in a X-component and a Y-component.

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