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The length of a vector (commonly known as the magnitude) allows us to quantify the property of a given vector. To find the length of a vector, simply add the square of its components then take the square root of the result. In this article, we’ll extend our understanding of magnitude to vectors in three dimensions.
17 Σεπ 2022 · Definition \(\PageIndex{2}\): Length of a Vector. Let \(\vec{u} = \left[ u_{1} \cdots u_{n} \right]^T\) be a vector in \(\mathbb{R}^n\). Then, the length of \(\vec{u}\), written \(\| \vec{u} \|\) is given by \[\| \vec{u} \| = \sqrt{ u_{1}^2 + \cdots + u_{n}^2}\nonumber \]
In physical science and engineering, a vector is a geometric object which has both magnitude or length and direction. A vector is commonly represented by a line segment in a specific direction, indicated by an arrow.
29 Δεκ 2020 · A vector is a directed line segment. Given points P and Q (either in the plane or in space), we denote with → PQ the vector from P to Q. The point P is said to be the initial point of the vector, and the point Q is the terminal point. The magnitude, length or norm of → PQ is the length of the line segment ¯ PQ: ‖→ PQ‖ = ‖ ¯ PQ‖.
The magnitude (length) of the vector makes a right triangle with the two components of the vector, where the magnitude is the hypotenuse. Thus, to find the magnitude of the vector \(\vec A=(A_x,A_y)\) we can use the Pythagorean theorem:
Definition: Vector. A vector is a quantity with both magnitude and direction. We will frequently represent a vector quantity with an arrow, where the direction of the vector is the direction that the arrow points, and the magnitude of the vector is represented by the length of the arrow.
Vector, in physics, a quantity that has both magnitude and direction. It is typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity’s magnitude.
