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angle betw 2. Determine whether the vectors a and b are parallel, orthogonal or neither for the given a and b. a. a <2,-1, 3> and b = <4, 2, 5> b. a <2,-1, 3> and b = <-4, 2, -6> c. a = <2, -1, 3> and b = <5, 1, -3>

angle betw 2. Determine whether the vectors a and b are parallel, orthogonal or neither for the given a and b. a. a <2,-1, 3> and b = <4, 2, 5> b. a <2,-1, 3> and b = <-4, 2, -6> c. a = <2, -1, 3> and b = <5, 1, -3>

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.CR: Chapter Review
Problem 8CC
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Need help with question 2, thank you.

1. For the vectors v = <1, 3, 2> and u = <3, 1, -1> a. Find v-u b. Find ||v|| and ||u|| c. Find the angle between v and u. 2. Determine whether the vectors a and b are parallel, orthogonal or neither for the given a and b. a. a <2,-1, 3> and b = <4, 2, 5> b. a = <2,-1, 3> and b = <-4, 2, -6> c. a = <2,-1, 3> and b = <5, 1, -3> 3. Find the cross product u X v when u = <0, 1, 3> and v = <3, 0, 1>. 4. Find an equation for the plane through (1, 3, 4), with normal vector <1, 3, -2>. 5. Find parametric equations for the line through the points (1, 3, 0) and (2, 4, 4). 6. Find an equation for the plane though the point (1,-1, 4) and parallel to the plane 2x + y + z = 1. 7. Find the tangent vector r' (t) and unit tangent vector T(t) at the point with t = 1 for r(t) = <cos nt, sin nt, t² + t>. 8. Find the length of the curve r(t) = <2cos t, 2sin t, t> from t = 1 tot = 5. 9. Find the curvature of the curve r(t) = <2cos t, 2sin t, t> at time t. 10. Find s(t), the length of the curve r(t) =<4cos t, 4sin t, 3t> from time 0 to t. What is the speed s'(t) of an object moving along this curve if r(t) represents its position at time t.
Transcribed Image Text:1. For the vectors v = <1, 3, 2> and u = <3, 1, -1> a. Find v-u b. Find ||v|| and ||u|| c. Find the angle between v and u. 2. Determine whether the vectors a and b are parallel, orthogonal or neither for the given a and b. a. a <2,-1, 3> and b = <4, 2, 5> b. a = <2,-1, 3> and b = <-4, 2, -6> c. a = <2,-1, 3> and b = <5, 1, -3> 3. Find the cross product u X v when u = <0, 1, 3> and v = <3, 0, 1>. 4. Find an equation for the plane through (1, 3, 4), with normal vector <1, 3, -2>. 5. Find parametric equations for the line through the points (1, 3, 0) and (2, 4, 4). 6. Find an equation for the plane though the point (1,-1, 4) and parallel to the plane 2x + y + z = 1. 7. Find the tangent vector r' (t) and unit tangent vector T(t) at the point with t = 1 for r(t) = <cos nt, sin nt, t² + t>. 8. Find the length of the curve r(t) = <2cos t, 2sin t, t> from t = 1 tot = 5. 9. Find the curvature of the curve r(t) = <2cos t, 2sin t, t> at time t. 10. Find s(t), the length of the curve r(t) =<4cos t, 4sin t, 3t> from time 0 to t. What is the speed s'(t) of an object moving along this curve if r(t) represents its position at time t.
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