Although there are many correct answers, for this WebAssign problem you must use exactly the given vector and point.

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1 Vector Lines: Basic ( ) Due: Mon Nov :01 AM MST Question Instructions Read today's Notes and Learning Goals. 1. Question Details vectors III DGB 0 [ ] A line is given in vector form: r(t) = r 0 + t v Which of the following is the direction vector for the line? r 0 v Which of the following represents a point on the line? r 0 v 2. Question Details vectors III DGB 1 [ ] A line is given in vector form: r(t)= 3, 2 + t 1, 5 Which of the following is the direction vector for the line? 3,2 1,5 Neither of these. Which of the following represents a point on the line? 3,2 1,5 Neither of these. 3. Question Details vectors III question 1 [ ] Write the vector form of the line parallel to v = 1, 2 and passing through the point P = ( 1,3). Write the equation in the form r(t)= x 0, y 0 + t a, b Although there are many correct answers, for this WebAssign problem you must use exactly the given vector and point. r(t)=

2 4. Question Details vectors III DGB WS 2 [ ] Download and complete Worksheet #2. If you are working in class get a copy from your instructor. Which of the following are correct direction vectors for the line? Select all that apply. 1,2 4,2 1, 2 4, 2 Which of the following represent points on the line? Select all that apply. 1,2 4,2 1, 2 4, 2 Which of the following are correct vector forms of the equation of the line? Select all that apply. 1,2 + t 4,2 1,1 + t 4,2 1,2 + t 4, 2 1,1 + t 4, 2 5. Question Details vectors III question 2 [ ] Which of the following vector equations correctly represent the line that is parallel to v = 1, 2, and that passes through the point (2,3)? Select all that apply. r(t) = 2,3 + t 1, 2 r(t) = 1, 2 + t 2, 3 r(t) = 2 + t, 3 2t r(t) = t, 2 r(t) = 2, 3 + t 2, 4

3 6. Question Details vectors III question 10 [ ] A line has vector form r(t) = t 2, 0 + 3, 5. Find the coordinate functions. x = 7. Question Details vectors III question 9 [ ] The coordinate functions of the line parametrized by: r(t) = 6t 1, 9t + 2. are: x(t) = The ycoordinate of the line, as a function of t, is: y(t) =

4 8. Question Details vectors III question 4 [ ] Suppose that the line r(t) = r 0 + v has coordinate functions x = 2t + 7 t 4 Which of these is the correct direction vector? 2, 1 2, 4 7, 1 7, 4 Which is of these represents a point on the line: 2, 1 2, 4 7, 1 7, 4 Write the vector equation of the line in the form r(t)= x 0, y 0 + t a, b using exactly the position and direction vectors you found above. r(t) = 9. Question Details vectors III question 5 [ ] Which of the following are correct vector equations for the line passing through the points (1, 1) and (3,6)? Select all that apply. r(t) = 1, 1 + t 3, 6 r(t) = 1, 1 + t 2, 7 r(t) = 3,6 + t 1, 1 r(t) = 3,6 + t 2, 7

5 10. Question Details vectors III question 5b [ ] Select the correct vector equation for the line passing through the points (1, 1) and (3,6), so that r(1) = 3,6. r(t) = 1, 1 + t 3, 6 r(t) = 1, 1 + t 2, 7 r(t) = 3,6 + t 1, 1 r(t) = 3,6 + t 2, 7 Find the coordinate functions for your choice. x = 11. Question Details vectors III question 5c [ ] Find the only vector equation for the line passing through the points (1, 1) and (3,6), so that r(0) = 3,6, and r(1) = 1, 1. Write your answer in the form r(t)= x 0, y 0 + t a, b r(t) = 12. Question Details vectors III question 6 [ ] Which of the following represent lines that pass through the origin? Select all that apply. r(t) = t 1, 5 r(t) = t 6, 1 2 r(t) = 2, 7 + t 3, 1 r(t) = 2, + t 4, none of the above.

6 13. Question Details vectors III question 7 [ ] Which of the following represent lines that are parallel to the line r(t) = 8, 2 + t 3, 1 Select all that apply. r(t) = 3t + 12, t 17 r(t) = 7 3t, 1 + t r(t) = 3t + 5, t+2 r(t) = 5t 3, 2t + 1 r(t) = 6t, 2t 14. Question Details vectors III question 12 [ ] There is only one vector equation for the line passing through the points (0,1) and (2, 1)), so that r(0) = 0,1, and r(1) = 2, 1. Find this vector equation. Then find its component functions: x = 15. Question Details vectors III WS3 [ ] Download and complete Worksheet #3. If you are working in class get a copy from your instructor. Compute the yintercept of the line you graphed.

7 16. Question Details vectors III question 16 [ ] A line is given in vector form by r(t) = t 2, 4 + 2, 5 What is the slope of the line? m = What is the yintercept of the line? b = What is the equation of the line in slopeintercept form, mx + b? 17. Question Details vectors III question 17 [ ] A line has vector equation r(t) = 3t 1, 5t + 4 What is the slope of the line? m = What is the yintercept of the line? b = What is the equation of the line in slopeintercept form, mx + b?

8 18. Question Details vectors III question 14 [ ] A particle is traveling along a straightline path in the plane. Its position at time t is given by: r(t) = 2, 4 + t 3, 6 At what time t will the particle pass through the point (2, 4)? t = At what time t will the particle pass through the point (5, 2)? t = What is the location R of the particle at time t = 10? R = A second particle is traveling along a different line given by s(t) = 1, 4 + t 2, 1 Find the values of the two parameters t r and t s in which the two lines intersect. Note: If the two paths intersect, the values of their parameters t r and t s need not be the same. If this particle's path intersects the path of the first particle (vector r) enter the values of the two parameters separated by a comma, otherwise enter 'none' if the particle's paths do not intersect. A third particle is following a line given by s(t) = 6t + 11, 12t + 1 If this particle's path intersects the path of the first particle (vector r) enter the values of the two parameters separated by a comma, otherwise enter 'none' if the particle's paths do not intersect. 19. Question Details vectors III question 18 [ ] Find a vector equation r(t) = r 0 + t v for the line with slopeintercept equation, 1. The line crosses the yaxis at t = v = 5 3 x + 2 4, that meets the following conditions: r(t) = Assignment Details

Graphical Solutions of Linear Systems

Graphical Solutions of Linear Systems Consistent System (At least one solution) Inconsistent System (No Solution) Independent (One solution) Dependent (Infinite many solutions) Parallel Lines Equations