## QUIZ 9

### Quiz 9 (Total 15p.) Show your work! 数学线上quiz代考

1. (1p.) Which of the points A(-4, 0, -1), B(3, 1, -5), and C(2, 4, 6) is closest to the yz-plane? Which point lies in the xz-plane?
1. (2p.) Find the lengths of the sides of the triangle PQR. Is it a right triangle? Is it an isosceles triangle? P(3, -2, -3), Q(7, 0, 1), R(1, 2, 1).
1. (1p.) Find equations of the spheres with center (2, -3, 6) that touch the xy-plane.
2. (2p.) Write inequalities to describe the region: The region between the yz-plane and the vertical plane x = 5.
1. (1p.) Find a vector a with representation given by the directed line segment AB. Draw AB and the equivalent representation starting at the origin: A(-2, 1), B(1, 2).
1. (1p.) Find the vector that has the same direction as <6, 2, -3> but has length 4.
2. (2p.) Find a + b, 4a + 2b, |a |, and |a b |: a = <-3, 4>, b = <9, -1>.
3. (2p.) Find the unit vectors that are parallel to the tangent line to the parabola y = x2 at the point (2, 4). 数学线上quiz代考
1. (3p.) A boatman wants to cross a canal that is 3 km wide and wants to land at a point 2 km upstream from his starting point. The current in the canal flows at 3.5 km/h and the speed of his boat is 13 km/h.(a) In what direction should he steer? (b) How long will the trip take?