13010004_Unit 7 MCV4U Grade 12 Calculus and vectors...

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Unit 7MCV4UGrade 12Calculus and VectorsTask 1:1. Determine the angle between each of the following pairs of vectors.(a).u=(2,4)v=(1,3)
θ=8°The angle betweenuvis 8°.(b).p=(1,4,5)q=(3,1,3)p∙q=(−1,4,5)(3,1,3)¿(1) (3)+(4) (1)+(5)(3)¿34+15¿7+15¿8|p|=(1)2+(4)2+(5)2=1+16+25=42|q|=(3)2+(−1)2+(3)2=9+1+9=19cosθ=p∙q|p||q|42¿¿19¿¿¿cosθ=8¿cosθ=8798cosθ=(0.2832)θ=cos1(0.2832)θ=74°The angle betweenpqis 74°.2. Find the slope of the vector that is perpendicular to scalar equation
3. Write an alternate vector equation for the following line. Change both the pointand the direction vector:
4. Determine whether the angle between each of the following pairs of vectors isacute, obtuse, or neither.(a).a=(10,4,1)b=(3,2,2)
The dot product is positive, so the angle between the vectors is acute.(b).p=(0,4,3)q=(7,2,1)p∙q=(0,4,3)(7,2,1)¿(0) (7)+(4) (2)+(−3)(1)¿083¿11The dot product is negative, so the angle between the vectors is obtuse.5. Given the vector equation of a line in 2-space,(x, y)=(3,2)+t(2,4).Write ascalar equation for the line.
6. Write a vector equation for the line that passes through the pointP(−1,0,3and is parallel to they-axis.)
(x, y ,z)=(1,0,3)+t(0,1,0).

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Term
Winter
Professor
No one
Tags
Vector Space, Dot Product, Euclidean vector, Vector Motors, Parametric equation, Surface normal

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