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Direction Of A Vector Formula – How To Find The Direction Of A Vector?

What is Direction of a Vector?

When two distinct vectors are directed from one to point to another, then it is called as the vector. They are usually differentiated in terms of speed or velocity. Mostly, we don’t get any clue about the direction here in which direction the object is moving. SO, we need a formula here to calculate the direction of a vector.

In physics, both magnitude or direction are given as the vector. Take an example of the rock, where it is moving at the speed of 5meters per second and direction is headed towards West then this is an example of the vector. So, let us have a quick discussion on vectors first. They are used to represent themagnitude and direction both.

For the things with quantities that are given by force or velocity, they could also be represented in the form of vectors. Both of them also have the direction or magnitude. Let us consider for some seconds, a force of about 5 Newtons is applied to a given direction at any point in the space. This is the point where force does not change itself for the applied force. It signifies that forces are independent of any point of application.

Direction of a Vector Formula

To apply the force in the right way, you should always know the magnitude and the direction. If x is the horizontal movement and y is the vertical movement, then the formula of direction is

\[\LARGE \theta =\tan^{-1}\frac{y}{x}\]

If (x1,y1) is the starting point and ends with (x2,y2), then the formula for direction is

\[\LARGE \theta =\tan^{-1}\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}\]

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