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Calc III (Vectors (Position Vector (Translating a vector into a position…
Calc III
Vectors
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Position Vector
A vector with an initial point at the origin of an x,y plane and a terminal point at P(V1, V2). Special note: ANY vector can be translated to a position vector
vector notation: <V1, V2 >
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Vector Length Notation
|| V || = sqrt[(V1)^2 + (V2)^2] Note: there is a half arrowhead written above the V. This notation specifies the length (or magnitude) only of the vector
Unit Vector
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To find the unit vector from any position vector, divide by its magnitude
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2 methods to find out if 2 vectors are the same. Need to know the length of the vector and the angle/slope of the vector.
Method 1: can use the distance formula and formula for slope on both vectors and check to see if they are the same for both. The slope formula tells you about the angle of the vector.
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Standard Basis Vector
i = < 1, 0 > Note that I has a " party hat" in the notation
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j = < 0, 1 > Note: j has a party hat in the notation
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Notice that i and j are position vectors because they begin at the origin but they are also unit vectors because they have a length of 1
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