WW-03.pdf - o(1 point Find the volume of the parallelepiped...

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Unformatted text preview: o (1 point) Find the volume of the parallelepiped defined by the vectors WW3 2 —2 —3 —2 , 2 , 5 —1 —4 —3 9 Consider the following geometry problems in 3-space Enter T or F depending on whether the statement is true or false. (You must enter T or F -- True and False will not work.) 1. A plane and a line either intersect or are parallel 2. Two planes orthogonal to a third plane are parallel 3. Two lines either intersect or are parallel 4. Two lines parallel to a third line are parallel 5. Two planes parallel to a third plane are parallel . Two planes parallel to a line are parallel . Two lines parallel to a plane are parallel . Two lines orthogonal to a plane are parallel GDW‘IO’) . Two planes either intersect or are parallel 10. Two planes orthogonal to a line are parallel 11. Two lines orthogonal to a third line are parallel e (1 point) Match the equations of the plane with one of the graphs below. 1.a:+y:2 2.wiz=2 3.m+y:—2 4.y7:z;=2 o (1 point) An implicit equation forthe plane passing through the points (3, —3, 2), (4, —4, —3), and (8, 0,1) is a (1 point) Give a vector parametric equation for the line through the point (5, —3, —2) that is parallel to the line (51;, —4 — t, 2t — 3): L(t) = e (1 point) The planes 3:13 — 5y — 22 : —27 and y — 53: + 52 : 15 are not parallel, so they must intersect along a line that is common to both of them. The vector parametric equation for this line is L(t) = (1 point) The plane that passes through the point (1, 1, 5) and is perpendicular to both :c+y—4z= 18and5y—53:+4z: —16 has as its implicit equation. 9 . Find the distance of the point (3, 6, —4) from the line r(t) : (1 + 2t, —1 -l— 3t, 7 — 2t). Answer: 9 Find the intersection of the lines r(t) : (—4 — 2t,10 —l— 2t,17 + 8t) and R(s) : {—9 + 58,15 — 58, s — 5). Write your answer as a point ((1,1), 6) where a, b, and c are numbers. Answer: (1 point) Determine whether the lines m—21_y—13 z—4 7 T 4 3 L12 and :1:+16 y+11 z+17 8 6 6 L22 intersect, are skew, or are parallel. If they intersect, determine the point of intersection; if not leave the remaining answer blanks empty. The lines ? v Point of intersection: ( , ,9 Find an equation of the plane consisting of all points that are equidistant from (-2, -5, 4) and (2, -3, -1), and having 4 as the coefficient of :13. Find the distance the point P(O, O, 1), is to the plane through the three points Q(2, 5, 0), R(3, 0, 1), and S(-2, 1, 3). e (1 point) A million years ago, an alien species built a vertical tower on a horizontal plane. When they returned they discovered that the ground had tilted so that measurements of 3 points on the ground gave coordinates of (0,0,0), (2, 2, 0), and (O, 2, 2). By what angle does the tower now deviate from the vertical? radians. @ (1 point) The axis of a light in a lighthouse is tilted, but the light shines perpendicular to its axis. When the light points east, it is inclined upward at 7 degrees. When it points north, it is inclined upward at 7 degrees. What is its maximum angle of elevation? Answer = degrees ...
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