Learning Outcome 2: Vectors, Lines and Planes
Understand vectors in two- and three-space, lines and planes in three-space, and be able to perform
associated computations.
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Performance Criteria:
- Find the distance between two points in R2 & nbsp; or R3.
- Give the vector from one point to another in R2 & nbsp; or R3, give the initial or terminal point of a vector. Determine the magnitude of a vector in R2 & nbsp; or R3.
- Read
- Watch
- Do
- Page 665: 5, 7, 3, 35, 36 Page 691: 5, 7, 10, 11, 12
- Add or subtract vectors, multiply a vector by a scalar, both algebraically and geometrically. Illustrate both the parallelogram method and tip-to-tail method for adding two vectors.
- Read
- Page 659: Figures 7, 9, 13, 20
- Watch
- This video from 3:20 to 5:00.
- This video up to 3:20. He calls the tip-to-tail method the "triangle method."
- Do
- Give the unit vector in the direction of a given vector. Determine whether two vectors are parallel.
- Read
- Page 658: Examples 1, 2, Figure 3
- Watch
- Do
- Page 666: 25, 27, 29 - 32 Page 691: 13, 15, 17
- Find a vector satisfying given direction and magnitude criteria. In particular, give a vector with a specified magnitude in the direction of a given vector, or in the perpendicular or opposite direction.
- Read
- Page 662: Example 5 Page 671: Example 2, 3
- Watch
- Do
- Page 666: 33, 37, 39, 40, 42, 43 Page 676: 9, 25, 27
- Find the dot product of two vectors, and know that it is a scalar. Determine whether two vectors are orthogonal (perpendicular), find a vector orthogonal to a given vector. Find the angle between two vectors.
- Read
- Page 678: below def. of dot product Page 680: Example 3
- Watch
- Do
- Page 684: 1 - 17 odd, 29, 31
- Find the projection of one vector on another, both algebraically and geometrically.
- Draw the vector components of a vector {\bf v} that are parallel and perpendicular to a vector {\bf b}. Find the vector components algebraically.
- Find the parametric equations or vector equation for a line
- through a given point and parallel to a given vector,
- through two given points in 2 or 3-space.
- Read
- Watch
- Do
- Page 677: 29 - 39 odd, 49
- Find the cross product of two vectors in 3-space. Know that the cross product of two vectors in 3-space is {\it a vector} that is orthogonal to both original vectors.
- Read
- Watch
- Do
- Page 695: 9, 11, 13, 15, 34
- Find the equation of a plane, given
- a point on the plane and a normal vector to the plane,
- three points on the plane.
- Read
- Watch
- Do
- Page 702: 1 - 7 odd, 11, 13 - 25 odd
- Determine whether two planes are parallel, perpendicular, or neither. Determine whether a line and a plane are parallel, perpendicular, or neither.
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