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Вы можете ознакомиться и скачать презентацию на тему Introduction to vectors. Доклад-сообщение содержит 31 слайдов. Презентации для любого класса можно скачать бесплатно. Если материал и наш сайт презентаций Mypresentation Вам понравились – поделитесь им с друзьями с помощью социальных кнопок и добавьте в закладки в своем браузере.

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Introduction to Vectors Karashbayeva Zh.O.

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What are Vectors? Vectors are pairs of a direction and a magnitude. We usually represent a vector with an arrow:

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Vectors in Rn

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Multiples of Vectors Given a real number c, we can multiply a vector by c by multiplying its magnitude by c:

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Adding Vectors Two vectors can be added using the Parallelogram Law

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Combinations These operations can be combined.

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Components To do computations with vectors, we place them in the plane and find their components.

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Components The initial point is the tail, the head is the terminal point. The components are obtained by subtracting coordinates of the initial point from those of the terminal point.

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Components The first component of v is 5 -2 = 3. The second is 6 -2 = 4. We write v =

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Magnitude The magnitude of the vector is the length of the segment, it is written ||v||.

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Scalar Multiplication Once we have a vector in component form, the arithmetic operations are easy. To multiply a vector by a real number, simply multiply each component by that number. Example: If v = , -2v =

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Addition To add vectors, simply add their components. For example, if v = and w = , then v + w = . Other combinations are possible. For example: 4v – 2w = .

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Unit Vectors A unit vector is a vector with magnitude 1. Given a vector v, we can form a unit vector by multiplying the vector by 1/||v||. For example, find the unit vector in the direction :

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Special Unit Vectors A vector such as can be written as 3 + 4. For this reason, these vectors are given special names: i = and j = . A vector in component form v = can be written ai + bj.