1. 2. 3. 4. 5. Find the component form of the vector , where P = (1, 3) and Q =

Question

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Find the component form of the vector , where P = (1, 3) and Q = (3, -5). The component form of is . (Simplify your answers.) Find the measures of the angles of the triangle whose vertices are A = (-3, 0), B = (3, 1), and C = (2, -1). The measure of is degree. (Round to the nearest thousandth.) The measure of is degree. (Round to the nearest thousandth.) The measure of is degree. (Round to the nearest thousandth.) Find the angle between the vectors u = -5i + 2j and v =-5i + 3j + 5k. The angle between the vectors is theta ? radians. (Round to the nearest hundredth.) Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. x2 + y2 + (z + 9)2 = 225, z = 0 Choose the correct description. The line through (12, 0, 0) and (0, 12, 0) The line through (12, 12, 0) parallel to the z-axis The circle with center (0, 0, 0) and radius 144, parallel to the xy-plane The circle with center (0, 0, 0) and radius 12, parallel to the xy-plane Describe the set of points in space whose coordinates satisfy the given inequalities or combinations of equations and inequalities. x2 + y2 + z2 = 4, y 0 x2 + y2 + z2 = 4, y 0 Choose the correct answer below. The hollow hemisphere cut from the sphere x2 + y2 + z2 = 4 by the xz-plane (the plane y = 0) located in the half-space defined by y 0; the hemisphere has radius 2 and is centered at (0, 0, 0) The solid hemisphere cut from the sphere x2 + y2 + z2 = 4 by the xz-plane (the plane y = 0) located in the half-space defined by y 0; the hemisphere has radius 2 and is centered at (0, 0, 0) The circle x2 + z2 = 4, y = 0, together with its interior The circle x2 + z2 = 4, y = 0 Choose the correct answer below. The circle x2 + z2 = 4, y = 0, together with its interior The hollow hemisphere cut from the sphere x2 + y2 + z2 = 4 by the xz-plane (the plane y = 0) located in the half-space defined by y 0; the hemisphere has radius 2 and is centered at (0, 0, 0) The circle x2 + z2 = 4, y = 0 The solid hemisphere cut from the sphere x2 + y2 + z2 = 4 by the xz-plane (the plane y = 0) located in the half-space defined by y 0; the hemisphere has radius 2 and is centered at (0, 0, 0)

Explanation / Answer

1) <2,-8> as PQ = (3,5) - (1,3)

2) angle ABC = 53.973

     angle BCA = 105.255

   angle CAB = 20.772

3) angle = 0.72 radian

4) option D

5) a) option B

b) option D

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