Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 13CR
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Question
Solve all Q16, 17, 18 explaining detailly each step
Transcribed Image Text:16. A vector perpendicular to both 2î + 2ĵ – k and -î + 2k is:
A. 3î + 4ĵ – 2k B. 3î – 4ĵ – 2k C. 2î + 3ĵ – 3k D. 4î + 3j
17. The parametric vector equations of two lines L1 and L2 are shown below
L¡: r= 4i+j – 2k + s(-4i – 2j – 2k) and
L2: r2 = 2i + 3j + 3k + t(2i + j + k).
Lines L and L2
A. Intersect
%3D
B. are parallel
C. are perpendicular
D. are in the same plane
18. A vector equation of a line through the points (2, 2, -1) and (0, -1, 2)
A. f = 2î + 2ĵ – k + t(2î – 3ĵ + 3k)
B. î = 2î + 2ĵ – k+t(-ĵ+ 2k)
C. f = -ĵ + 2k + t(2î+ 2ĵ – k)
D. f = -j + 2k + t(-2î – 3ĵ + 3k)
19. The Cartesian equations ofa line which passes through the point (2, -1, -3) and is parallel to
the vector 3î +ĵ – k are:
|
X-3
y-1
z+1
X-2
В.
3
y+1
Z-3
--1
-3
-1
- 1
X+2
C.
3
y-1
Z-3
X-2
y+1
z+3
D.
---
1
-1
3
- 1
and = =
X-1
у+2
Z-3
2х-1
у-1
2z+1
20. The cosine of the angle between the lines
1s:
%3D
1
3
2
3
3
-4
A.
V42
-3
B.
21
19
C.-
7V14
19
D.
14V14
21. A vector equation of line through the point with vector 3î- j and perpendicular to the line
f = 3ĵ + A(î – 3j) is:
A. Î = î – 3ĵ + H(31- i)
C. Î = 3î – ĵ + µ(3î + j) D. Î = 3î – î + µ(3î + j)
B. f = 3î - j +, u(3î - )
%3D
2x+1
y+2
4-z .
22. The line
is parallel to the line
3
2.
Z-1
x-+3
Á.
3
y+1
3
2
B. f = î – ĵ + 5k + t(3î + 3ĵ + 2k)
C. f = -î – 2î + 4k + t(-3î + 3ĵ - 2k)
D. f = 3k + t(3î + 6ĵ – 4k)
23. The Cartesian equation of the plane containing the point i + 3j – 8k and perpendicular to th
line; 7 = 3i + 7j – 2k + a(5i –j- 4k) is
%3D
A. 5x - y + 4z = 34
B. 5x – y - 4z = 34
D. 5x + y + 4z = 34
24. The vector equation of the plane containing the point with position vector î - 3k and normal
C. 5x + y - 4z = 34
to the vector î + 2ĵ + k is:
A. f(î – 3k) = -2
C. î = î – 3ĵ + A(î + 2ĵ + k) D. î = î + 2j + k + A(î – 3k)
25. A plane passes through the point (1, 2, 3) and is perpendicular to a straight line in the
direction of the vector 2i + 3i – 5k. A Cartesian equation of the plane is
B. f(î + 2î + k) = -2
%3D
A. 2x + 3y - 5z - 7 = 0
B. 2x + 3y + 5z + 7 = 0
%3D
69
||
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