Calculus and Vectors Unit 7 Key Questions - Unit 7 Key...

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Unit 7 Key Questions Task 1: Application Questions 1. Determine the angle between each of the following pairs of vectors. (10 marks: 5 marks each)
θ = cos 1 ( 0.2831 ) θ = 74 ° 2. Find the slope of the vector that is perpendicular to the scalar equation 6 x −3 y +2=0 . (2 marks)
3. Write an alternate vector equation for the following line. Change both the point and the direction vector: w =(4,−1,3)+ t (−2,1,7) (3 marks)
w → = ( 2,0,10 ) + t (− 4,2,14 ) 4. Determine whether the angle between each of the following pairs of vectors is acute, obtuse, or neither. (4 marks: 2 marks each) a . a →=(10,−4,1) b →=(3,−2,2)
5. Given the vector equation of a line in 2-space, ( x , y )=(3,2)+ t (2,4) , write a scalar equation for the line. (4 marks)
6. Write a vector equation for the line that passes through the point P (–1, 0, 3) and is parallel to the y -axis. (2 marks)
( x, y ,z ) = ( 1,0,3 ) + t ( 0,2,0 ) Task 2: Thinking Questions
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