1. Given and , provide a geometric argument of and

2. Find a vector in -plane with length and angle with respect to positive side of -axis.

3. Find a unit vector in opposite direction of

4. Suppose and are real numbers. Find a nonzero vector perpendicular to the vector .

5. Find the vector projection of onto

6. Find all values of such that the two vectors and are perpendicular to one another.

7. Find equation of a line passing the point and perpendicular to the plane

8. Find equation of a line passing the point and parallel to the line

9. Find equation of a line passing the points and .

10. Find the distance between the point and the line intersection of the planes and

11. Find the distance between the two planes and

12. Find the angle between two planes and

13. Find if the two lines intersect each other. If so, find the point of intersection.

(1)

(2)

14. Find equation of a plane containing the points .

15. Find equation of a plane that contains the line and is parallel to the plane

16. Find a unit vector that is perpendicular to and

17. Find the value of such that the two planes and are perpendicular to each other.

To see the notes, visit vector fundamentals part II.