# Calc10_3 - 10.3 Vector Valued Functions Greg Kelly Hanford...

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10.3 Vector Valued Functions Greg Kelly, Hanford High School, Richland, Washington

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Any vector can be written as a linear combination of two standard unit vectors. , a b = v 1,0 = i 0,1 = j , a b = v ,0 0, a b = + 1,0 0,1 a b = + a b = + i j The vector v is a linear combination of the vectors i and j . The scalar a is the horizontal component of v and the scalar b is the vertical component of v .
We can describe the position of a moving particle by a vector, r ( t ). ( 29 t r If we separate r ( t ) into horizontal and vertical components, we can express r ( t ) as a linear combination of standard unit vectors i and j . ( 29 ( 29 ( 29 t f t g t = + r i j ( 29 f t i ( 29 g t j

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In three dimensions the component form becomes: ( 29 ( 29 ( 29 ( 29 f g h t t t t = + + r i j k
Graph on the TI-89 using the parametric mode. MODE Graph……. 2 ENTER Y= ENTER xt1 t cos t yt1 t sin t = = WINDOW GRAPH ( 29 ( 29 ( 29 cos sin 0 t t t t t t = + r i j 8 π

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Graph on the TI-89 using the parametric mode. ( 29 ( 29 ( 29 cos sin 0 t t t t t t = + r i j MODE Graph……. 2 ENTER Y= ENTER xt1 t cos t yt1 t sin t = = WINDOW GRAPH
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