Direction of a Vector Mathematics Formula
Direction of a Vector Mathematics Formula with example when two distinct points are directed from one place to another then it is denoted by a vector. It can also be seen as differences between velocity and speed. no clue about in which direction the object is moving. Therefore, we use this formula that will enable us to know in which direction the object is moving. In physics, the magnitude and direction are expressed as a vector. If we say that the rock is moving at 5 meters per second, and the direction is towards the West, then it is represented using a vector. with example . when two distinct points are directed from one place to another then it is denoted by a vector. It can also be seen as differences between velocity and speed. no clue about in which direction the object is moving. Therefore, we use this formula that will enable us to know in which direction the object is moving. In physics, the magnitude and direction are expressed as a vector. If we say that the rock is moving at 5 meters per second, and the direction is towards the West, then it is represented using a vector.
so it is,
If x is the horizontal movement and y is the vertical movement, then the formula of direction is:
θ=tan−1yx
If (x1,y1 ) is the starting point and the ending point is (x2,y2 ), then the formula for direction is:
θ=tan−1(y2−y1)(x2−x1) then.
What are vector magnitude and direction?
We are used to describing vectors in component form. For the example, (3,4)(3,4)left parenthesis, 3, comma, 4, right parenthesis. We can plot vectors in the coordinate plane by drawing a directed line segment from the origin to the point that corresponds to vector’s components:
Considered graphically, there’s another way to uniquely describe vectors — their \blueD{\text{magnitude}}magnitudestart color #11accd, start text, m, a, g, n, i, t, u, d, e, end text, end color #11accd and \greenD{\text{direction}}directionstart color #1fab54, start text, d, i, r, e, c, t, i, o, n, end text, end color #1fab54:
yyxx(a,b)(a,b)\blueD{||\vec u||}∣∣u∣∣\greenD{\theta}θ
The \blueD{\text{magnitude}}magnitudestart color #11accd, start text, m, a, g, n, i, t, u, d, e, end text, end color #11accd of a vector gives the length of the line segment, while the \greenD{\text{direction}}directionstart color #1fab54, start text, d, i, r, e, c, t, i, o, n, end text, end color #1fab54 gives the angle the line forms with the positive xxx-axis.
The magnitude of vector \vec vvv, with, vector, on top is usually written as ||\vec v||∣∣v∣∣vertical bar, vertical bar, v, with, vector, on top, vertical bar, vertical bar.
Direction of a Vector Mathematics Formula with example
Example 1: Quadrant \text{I}Istart text, I, end text
Let’s find the direction of (3,4)(3,4)left parenthesis, 3, comma, 4, right parenthesis:
\tan^{-1}\left(\dfrac{4}{3}\right)\approx 53^\circtan−1(34)≈53∘tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, 4, divided by, 3, end fraction, right parenthesis, appDirection of a Vector Mathematics Formula with exampleroximately equals, 53, degrees
