SM10203 Mathematics ii

Chapter 1 : Vector i

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Scalars and Vectors

Scalar is a number which expresses quantity. Examples: mass, volume, energy, money

Vector is a quantity which has both magnitude and direction. The magnitude of a vector is a scalar.Examples: displacement, velocity, acceleration, electric field

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Vector are represented by directed line segment.

Length of the line segment is the magnitude of the vector.

Direction of the line segment is the direction of the vector.

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Same vector - Line segment with the same length and direction.

In each case the vector start a specific point then moves 2 units to the left and 5 units up.

Notation :

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Position vector -

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The general notation for a n-dimensional vector is

The i-unit vector points in the positive x-direction.

The j-unit vector points in the positive y-direction.

The k-unit vector points in the positive z-direction (upward).

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Vector Arithmetic

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Vector subtraction : Subtract “b” from “a”.

Graphically,Method 1: add the negative of “b” to “a”.Draw a vector from the start of “a” to the end of “b”. This is the resultant vector.

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Method 2

Start vector “b” at the start of vector “a”.Then draw the resultant vector from the end of “b” to the end of “a”.

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Dot Product

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Dot Product

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Dot Product

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Dot Product

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Cross Product

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Cross Product

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Cross Product

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Cross Product

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Cross Product

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Cross Product

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Right Hand Rule

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Cross Product

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Cross Product

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Cross Product

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Cross Product

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