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6.3 Vector in the Plane Magnitude Component form Unit Vector
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Vector is a Directed Line Segment Terminal point Initial point Magnitude ( or Length): || PQ ||
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Let P = (0,0) and Q = (3,4) To find the Magnitude || PQ || Direction (slope) is always important. Slope of
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Vectors equality If two vectors equal if they have the same magnitude and direction.
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is a vector in standard position Vectors in Standard position have an initial point at the origin (0, 0).
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Component Form of a vector P = (p 1, p 2 ); Q = (q 1, q 2 ) Which can be labeled by just a letter.
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Vector “V” can renamed If || V || = 1, then V is a Unit Vector. || V || = 0 iff V is 0
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Find the Component form and Magnitude Let
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Find the Component form and Magnitude Let
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Find the Component form and Magnitude Let
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Vector Operations Scalar Multiplication Let
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Vector Operations Vector Addition Let
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Parallelogram Law used in Addition of Vectors Graph the Vectors move the tail of one vector to the head of the other vector.
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Parallelogram Law used in Addition of Vectors Graph the Vectors move the tail of one vector to the head of the other vector.
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Properties of Vectors U + V = V + U (Comm.) (U + V) + W = U + (V + W)(Asso.) U + 0 = U(Identity) U + (-U) = 0(Inverse) C(DU)=(CD)U(Comm.) (C + D)U = CU + DU(Dist.) 1(U)=U;0(U)=0 || cV|| =|c| x ||V||
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How to Find the Unit Vector Let
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Standard Unit Vector Writing the Unit Vector as Standard Unit Vector. i = j =
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Direction Angle of a Unit Vector What is the coordinate of the intersection of the vector and unit circle?
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Direction Angle of a Unit Vector What is the slope of the vector? What function Is rise over run?
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Direction Angle of a Unit Vector What is the slope of the vector? What function Is rise over run?
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Direction of a Vector can be found if it is not a Unit Vector
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Homework Page 436 – 437 # 1, 7, 15, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73
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Homework Page 436 – 437 # 32, 38, 54, 62, 70, 80
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