Directed Line Segment: VECTORS • A line segment with direction is called a directed line segment. • If ‘A’ and ‘B’ are two distinct points in the space‚ then the ordered pair (A‚ B) is called as a directed line segment and is denoted by """""# . ! • In """""# ‚ ‘A’ is called initial point and ‘B’ is called terminal ! point of """""# . ! • The distance from ‘A’ to ‘B’ is called the length or magnitude of """""# . The length or magnitude of """""# ! ! is denoted by ’"""""# ’. Thus
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quantity which depends on direction a vector quantity‚ and a quantity which does not depend on direction is called a scalar quantity. Vector quantities have two characteristics‚ a magnitude and a direction. Scalar quantities have only a magnitude. When comparing two vector quantities of the same type‚ you have to compare both the magnitude and the direction. For scalars‚ you only have to compare the magnitude. When doing any mathematical operation on a vector quantity (like adding‚ subtracting‚ multiplying
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MCV4U0 Vector Applications Name:__________________ Date:______________ 1. A ship sailing on the open sea leaves Port A for Port B at a bearing of N25oW. A wind of 6 km/h on a bearing of N10oE blows the ship off course. If the ship is capable of 35 km/h in still water‚ find the new speed and direction relative to the shore. 2. A boat is capable of 20 km/h in still water. You wish to cross the river to a point directly across from your present position. At what angle to the bank should
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Vector Analysis Definition A vector in n dimension is any set of n-components that transforms in the same manner as a displacement when you change coordinates Displacement is the model for the behavior of all vectors Roughly speaking: A vector is a quantity with both direction as well as magnitude. On the contrary‚ a scalar has no direction and remains unchanged when one changes the coordinates. Notation: Bold face A‚ in handwriting A . The magnitude of the vector is denoted by A A
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a stochastic process with the following properties: (a.) The number of possible outcomes or states is finite. (b.) The outcome at any stage depends only on the outcome of the previous stage. (c.) The probabilities are constant over time. If x0 is a vector which represents the initial state of a system‚ then
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Sciences ECE / ICE / MexE Department ECE 352 VECTOR ANALYSIS DEL OPERATOR GROUP 3 Andaya‚ Rizalyn Ramos‚ Maria Issa P. ∇ Del is a symbol used in mathematics‚ in particular‚ in vector calculus‚ as a vector differential operator‚ usually represented by the nabla symbol ∇. Del may denote the gradient (locally steepest slope)‚ the divergence of a vector field‚ or the curl (rotation) of a vector field. The symbol ∇ can be interpreted as a vector of partial derivative operators‚ and its three
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Pure Mathematics – Unit 1 Vectors Find the magnitude and direction of the vectors – 3i + 4j‚ -5i + 12j‚ -10j‚ i – j The vector XY has magnitude 10 units and is inclined at 300 to the x-axis. Express XY as a column vector The vector PQ has magnitude 5 units and is inclined at 1500 to the x-axis. Express PQ as a column vector Find numbers m and n such that m 35 + n 21= 49 If a = 38+ λ and b = λ3 where a and b are parallel‚ find λ. The position vectors of points A and B are 2-1
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Experiment 3 Vectors J. Rodriguez‚ J. Panis‚ Y.Magsipoc‚ A. Castillo‚ A. Ordoñez‚ M. Tombado‚ J. Semilla‚ K. Almeniana‚ and P. Bugacia Industrial Engineering Department‚ College of Engineering Adamson University‚ Ermita‚ Manila In this experiment‚ the students will determine the resultant of different forces using different methods: graphical method; and getting the equilibrant of forces using component method the force table. Each of the three methods has their own way of getting the resultant
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1. Gradient of a scalar field function Scalar Function: Generally‚ What Is Scalar Function? The Answer Is that a scalar function may be defined as A function of one or more variables whose range is one-dimensional‚ as compared to a vector function‚ whose range is three-dimensional (or‚ in general‚ -dimensional). Scalar Field When We Talk about Scalar Field‚ We Are Talking about the Scalar Function Being Applied to a Space (More like Euclenoid Space etc) or‚ a scalar field associates
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through the point with coordinates (2‚ 1). What is the perpendicular distance from the origin to the line with equation ? 3) Solve the inequality 2 4)Consider the vectors a = i − j + k‚ b = i + 2 j + 4k and c = 2i − 5 j − k. (a)Given that c = ma + nb where m‚ n ‚ find the value of m and of n. (5) (b)Find a unit vector‚ u‚ normal to both a and b. (5) (c)The plane 1 contains the point A (1‚ –1‚ 1) and is normal to b. The plane intersects the x‚ y and z axes at the points L‚ M and N respectively
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