The equation of plane through (3,-1,7) and perpendicular to the vector (4,2,-5) is4x + 2y5z - 25 = 0.FalseTrue O

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Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 7E

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We mentioned in Section 7.5 that our algebraic treatment of vectors could be attributed, in part, to the Irish mathematician William Rowan Hamilton. Hamilton considered his greatest achievement to be the discovery of qualernions, which he (incorrectly) predicted would revolutionize physics. Research the subject of quaternions. What are they? Why did quaternions fail to be as useful for physics as Hamilton predicted? How are quaternions useful, instead, for 3.D computer graphics? Write a paragraph or two about your findings.
Take this test to review the material in Chapters 4and Chapters 5. After you are finished, check your work against the answers in the back of the book. Write w=(7,2,4) as a linear combination of the vectors v1, v2 and v3 if possible. v1=(2,1,0), v2=(1,1,0), v3=(0,0,6)
Find the equation of the plane that passes through the point (−2, 8, 4) and contains vectors ⃗a (2,4,6) and ⃗b(4, -2,6)
Find the equation of the plane that is parallel to the vectors <1, 1, 2> and contains thepoints (–2, 3, –1) and (2, 0, 1)
Find the equation of the line that passes through the point (3,4,5) and is parallel to the vector product of the vectors (1,3, -5) and (-3,1,4).
what is the vector equation of the line of intersection of the planes z=5 and x=9
What is the vector equation of the line segment that connects point P(1,−1,2) to point Q (4,1,7)?
Find an equation of the plane through the point and perpendicular to the given vector. (8, 2, 3)‹-3, 1, 5›
Give the parametric and symmetric equations of the line that passes through the point (5,−1,3) and is perpendicular to both vectors ⟨2,6,−1⟩ and ⟨−4,3,−5⟩
5. Find the equation of the plane that is parallel to the vectors 3,0,1 and 0,1,2, passing through the point (1,0,−4).
Suppose that a plane contains the points (5, 0, 0) and (0, 3, 1) and the line with the vector equation r = t < 2.5, 1.5, 0.5 >. What is the equation of the line? Please explain your steps and show work.
If the equation of a plane is given by 2x - 10y + 11z = 30 What is a normal vector to the plane? [2, -10, 11] [15, -10, 11] [-15, -10, 11] [-15, 10, -11]

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The equation of plane through (3,-1,7) and perpendicular to the vector n(4,2,-5) is 4x + 2y5z-25 = 0. False True O