Lucas does not like Dustin weapon and decides to design his own. His model has a plane that contains the poi A(-5,2,-4) and two direction vectors, AB = (4,8,1) and AC = (-3,-2,0). Which of the following statement about this plane is/are true? Justify your answer. i. The plane has a parametric equation that can be defined as follows: (x = -5+4t - 3s y = 2+8t - 2s z = −4+t ii. The plane has a vector equation that can be defined as (x, y, z) = (-5,2,-4) + t(3,2,0) + s(4,8,1) iii. The point D(31,6,0) lies on the plane iv. The z-intercept of the plane is 0,0,-5)

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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Lucas does not like Dustin weapon and decides to design his own. His model has a plane that contains the point
A(-5,2,-4) and two direction vectors, AB (4,8,1) and AC = (-3,-2,0). Which of the following statement(s
about this plane is/are true? Justify your answer.
i. The plane has a parametric equation that can be defined as follows:
(x = -5 +4t-3s
y = 2+8t - 2s
z = -4+t
ii.
The plane has a vector equation that can be defined as (x, y, z) = (-5,2,-4) + t(3,2,0) +
s(4,8,1)
iii. The point D(31,6,0) lies on the plane
iv. The z-intercept of the plane is 0,0,-5)
---
Transcribed Image Text:Lucas does not like Dustin weapon and decides to design his own. His model has a plane that contains the point A(-5,2,-4) and two direction vectors, AB (4,8,1) and AC = (-3,-2,0). Which of the following statement(s about this plane is/are true? Justify your answer. i. The plane has a parametric equation that can be defined as follows: (x = -5 +4t-3s y = 2+8t - 2s z = -4+t ii. The plane has a vector equation that can be defined as (x, y, z) = (-5,2,-4) + t(3,2,0) + s(4,8,1) iii. The point D(31,6,0) lies on the plane iv. The z-intercept of the plane is 0,0,-5) ---
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