where s, t E R. The plane contain the points P(1,-1,-4) and Q(2,1,-3). Moreover, contains the line I =y+3=21 Determine the general equation of the plane 2. Also, sketch the graph of 2.
where s, t E R. The plane contain the points P(1,-1,-4) and Q(2,1,-3). Moreover, contains the line I =y+3=21 Determine the general equation of the plane 2. Also, sketch the graph of 2.
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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Question
4
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Transcribed Image Text:1. B
Consider A = 8i - 12j, B = 2i + 14j and C = 18i - 10j.
(a) In R² space, draw the vectors A, B, and C in position representation.
(b) Find the unit vector having the same direction as 6A + 3B.
(c) Find scalars z and y such that zA-yB=-C.
2.
Let A = (1,-1,0) and B=(2, 1,-2).
(a) Solve for projgA.
(b) Find the angle between projgA and A.
3.
Give the parametric and symmetric equations of the line that passes through
the point (2,3,-1) and is perpendicular to both lines L₁ and L₂
z = 1+t
z=1
L1:y=3t
and L2 y = −3+3s
z=1-t
2=8
where s, t E R.
4.
The plane contain the points P(1,-1,-4) and Q(2, 1,-3). Moreover, it
contains the line
I
y +3=
2
3
Determine the general equation of the plane 2. Also, sketch the graph of .
5.
IDENTIFY and SKETCH the graph of the following equations in R³.
Make sure to rewrite the equations in standard form.
(a) x² + y² + 2²-2r-2ky-z+k²+ = 0, where k>0
(b) 2:³0. Show the trace you use.
=
(c) 9x² + y² + 3622-18-72z+28= 0. Show the traces as well.
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