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3. (10) Find the following vectors. • The vector with initial point (1, 1, 1), a length of 3, and which points toward (1, 3, 5). • A vector that has the same direction as the one that runs from the point (1, 0, -1) to the point (3, 2, -4), but which is only half as long. • A vector that has positive x- and y- components, a z- component of 4, and which has a norm of 10. 4. (10) Let u = < 2, -3, 1 >, v = < 0, 1, -1 >, and w = < 6, -2, 3 >. Compute the following: • (v · w)u • (2u - 3v) · w • v × w • w × u / ||u × v|| 5. (10) Find the direction angles for the vector v = < 0, 1, -3 >. Round your answers to the nearest whole degree. 6. (10) Find a set of parametric equations for the line that passes through the points (-1, 2, 1) and (3, -2, 1). 7. (10) Find the equation of the plane that contains the points (1, 3, 2), (-2, 0, 2), and (1, 4, 3).

          3. (10) Find the following vectors.
• The vector with initial point (1, 1, 1), a length of 3, and which points toward (1, 3, 5).
• A vector that has the same direction as the one that runs from the point (1, 0, -1) to the point (3, 2, -4), but which is only half as long.
• A vector that has positive x- and y- components, a z- component of 4, and which has a norm of 10.

4. (10) Let u = < 2, -3, 1 >, v = < 0, 1, -1 >, and w = < 6, -2, 3 >. Compute the following:
• (v · w)u
• (2u - 3v) · w
• v × w
• w × u / ||u × v||

5. (10) Find the direction angles for the vector v = < 0, 1, -3 >. Round your answers to the nearest whole degree.

6. (10) Find a set of parametric equations for the line that passes through the points (-1, 2, 1) and (3, -2, 1).

7. (10) Find the equation of the plane that contains the points (1, 3, 2), (-2, 0, 2), and (1, 4, 3).

3. (10) Find the following vectors.
• The vector with initial point (1, 1, 1), a length of 3, and which points toward (1, 3, 5).
• A vector that has the same direction as the one that runs from the point (1, 0, -1) to the point (3, 2, -4), but which is only half as long.
• A vector that has positive x- and y- components, a z- component of 4, and which has a norm of 10.

4. (10) Let u = < 2, -3, 1 >, v = < 0, 1, -1 >, and w = < 6, -2, 3 >. Compute the following:
• (v · w)u
• (2u - 3v) · w
• v × w
• w × u / ||u × v||

5. (10) Find the direction angles for the vector v = < 0, 1, -3 >. Round your answers to the nearest whole degree.

6. (10) Find a set of parametric equations for the line that passes through the points (-1, 2, 1) and (3, -2, 1).

7. (10) Find the equation of the plane that contains the points (1, 3, 2), (-2, 0, 2), and (1, 4, 3).

Added by Dennis C.

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