https://www.sinmath.com/topic/vector/Recent content in Vector on Mathematics Learning PortalHugo -- gohugo.io© {year} | Mathematics Learning PortalTue, 30 Jan 2024 19:46:51 +0700https://www.sinmath.com/vector-orthogonal-projection/Tue, 30 Jan 2024 19:46:51 +0700https://www.sinmath.com/vector-orthogonal-projection/In this article we will discuss vector projections, especially orthogonal (perpendicular) vector projections. Orthogonal projection of a vector onto another vector, the result is a vector. Meanwhile, the length of the projection of an orthogonal vector on another vector is always a positive real number/scalar. The orthogonal projection of vector $\vec{u}$ on vector $\vec{v}$ can be denoted by ${\vec{u}}_{\vec{v}}$ or $\vec{p}$ and is defined by the following argument. Proposition: Projeksi scalar orthogonal $\vec{u}$ falls on $\vec{v}$ adalah $$\left| \left| \vec{p}\right| \right|=\frac{\vec{u}\cdot\vec{v}}{\left| \vec{v}\right|}$$ The projection of the vector $\vec{u}$ onto the vector $\vec{v}$ is the vector $${\vec{u}}_{\vec{v}}=\left( \frac{\vec{u } \cdot \vec{v}}{\left|.https://www.sinmath.com/application-of-vectors-in-life/Tue, 30 Jan 2024 03:02:30 +0700https://www.sinmath.com/application-of-vectors-in-life/In this article we will discuss several applications of vectors, namely Resultant Vectors, Normal Vectors, Orthogonal Projections of Vectors, Distance from point to line, and Area and Volume. 1. Result of Two Vectors Look at the image on the side below. Given two vectors, namely vectors $\vec{a}$ and $\vec{b}$ and the angle formed by vector $\vec{b}$ with respect to vector $\vec{a}$, namely $\alpha $. The resultant of the vectors $\vec{a}$ and $\vec{b}$ is the same as finding the length of OC.https://www.sinmath.com/vector-cross-multiplication-cross-multiplication/Mon, 29 Jan 2024 23:31:26 +0700https://www.sinmath.com/vector-cross-multiplication-cross-multiplication/One thing that only applies to the three-dimensional vector space R3 is cross vector (vector multiplication between 2 vectors), namely the multiplication between 2 vectors which produces a single vector. Cross product or cross product is the product of two vectors in three-dimensional space (R3) which produces a vector perpendicular to the two vectors being multiplied. Or it can also be said that the cross product between two vectors will produce a new vector whose direction is perpendicular to each vector.https://www.sinmath.com/dot-product-scalar-multiplication-of-two-vectors/Sun, 28 Jan 2024 15:35:32 +0700https://www.sinmath.com/dot-product-scalar-multiplication-of-two-vectors/In this article we will learn about operations on vectors, namely vector multiplication or dot product or dot product. After previously we learned operations on vectors, namely addition and subtraction on vectors↝ and multiplication of vectors with scalars↝ , so this time we will continue with the discussion of Vector Dot Multiplication (Dot Product). We can present vectors in algebraic form and geometric form where two vectors will form a certain angle.https://www.sinmath.com/comparison-of-vectors-on-line-segments/Fri, 26 Jan 2024 19:17:11 +0700https://www.sinmath.com/comparison-of-vectors-on-line-segments/In this article we will learn about Vector Comparison of Line Segments. This vector comparison is actually the same as scalar multiplication with vectors which we have studied in the article Geometric Interpretation of the Position of Two or More Vectors↝ . This time we will study in more depth the coordinates of the dividing points. There are three things we will learn in the Vector Comparison material, namely being able to determine the division of a line segment using the ratio m:n, determining the division formula in vector form and determining the coordinates of the dividing points on line segments and vectors.https://www.sinmath.com/vectors-in-r3-space-three-dimensional-space/Mon, 22 Jan 2024 16:56:15 +0700https://www.sinmath.com/vectors-in-r3-space-three-dimensional-space/After previously studying vectors in the plane (R2), next we will develop our discussion regarding vectors in geometric shapes (R3). Vectors in geometric shapes (three dimensions) are vectors that have 3 axes, namely X, Y and Z, which are perpendicular to each other and the intersection of the three axes as the base. 1. Vector Writing in R3 Vectors in space are vectors that are located in 3-dimensional space. This space is formed by 3 axes, namely the X axis, Y axis, and Z axis.https://www.sinmath.com/vector-algebra-in-plane-figures-2-dimensional-space/Fri, 19 Jan 2024 12:53:32 +0700https://www.sinmath.com/vector-algebra-in-plane-figures-2-dimensional-space/A two-dimensional vector is a vector that has two elements, namely vertical (Y-axis) and horizontal (X-axis). Vectors in a plane (dimensional two) are characterized by an X-axis and a Y-axis, which intersect at the center point O (0, 0). Analytically, two-dimensional vectors can be presented according to their elements, namely: $\vec{\text{a}}=\begin{pmatrix}x \\\\ y \\\\ \end{pmatrix}$ atau $\vec{\text{a}}=\left( x,y \right)$atau kombinasi linear $\vec{\text{a}}=x\widehat{i}+y\widehat{j}$ Where x is the horizontal element. When $x > 0$ (positive) then x has a direction to the right and when $x < 0$ (negative) x has a direction to the left.https://www.sinmath.com/geometric-interpretation-of-the-position-of-two-or-more-vectors/Wed, 10 Jan 2024 19:12:16 +0700https://www.sinmath.com/geometric-interpretation-of-the-position-of-two-or-more-vectors/1. Inline (collinear) vectors Points P, N, and Q are said to be collinear if the vector constructed by two points between them can be expressed as the vector product of the other two points. Thus, if the points P, N and Q lie on a straight line, N is said to divide the line segment PQ in the ratio k, if $\overrightarrow{PN}~=k\text{ }\overrightarrow{NQ}$. Definition of inline (collinear) points Three points P, N, and Q are said to be collinear if and only if $(\Leftrightarrow )$https://www.sinmath.com/geometric-vector-operations/Sat, 06 Jan 2024 12:48:56 +0700https://www.sinmath.com/geometric-vector-operations/1. Addition of Two Vectors The sum of two or more vectors is called the result vector or resultant. Geometrically, there are 2 rules for adding two vectors, namely: Triangle rule Parallelogram rule On Vector summation occurs: Commutative property $ \overline{a}+\overline{b}=\overline{b}+\overline{a} $ Associative properties $ \left( \overline{a}+\overline{b} \right)+\overline{c}=\overline{a}+\left( \overline{b}+\overline{c} \right) $ Identity element, namely the zero vector $ \overline{a}+\overline{0}=\overline{a}=\overline{0}+\overline{a} $ Inverse add $ \overline{a}+(-\overline{a})=\overline{0} $ 2.https://www.sinmath.com/vector-concepts-and-several-types-of-vectors/Fri, 05 Jan 2024 22:41:20 +0700https://www.sinmath.com/vector-concepts-and-several-types-of-vectors/1. Understanding scalar and vectors In everyday life, we find a lot of quantities, such as the length of a stick, the volume of a can, the area of ​​a garden, the amount of electric charge, the mass of an object and so on.The quantities are usually expressed by a number accompanied by the unit of amount.Such a large amount, called scalar. If we move or shift an object (material) in any form, the transfer of the object will meet two elements, namely how far the move and in which direction the object moves.