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

This preview shows pages 1–3. Sign up to view the full content.

WW 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern