7. 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)
7. 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)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Answer the question in the space provided and in full details. Show ALL your steps and your calculations. Answer in, with therefore statements
Transcribed Image Text:7. 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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