33. Sketch the diagram that you would use to find the magnitude of the sum of a and b if the angle between them is 67° and the magnitudes are 7 and 11 respectively. Ensure that all vectors are labelled. Also include the equilibrium vector in your diagram. 34. For the function whose graph is given below, find the following: [ a. lim f(x)= x-2 b. lim f(x)= x-2° c. lim f(x)= x 2 d. lim f(x)= e. lim f(x)= x-1 f. lim f(x)= x1 g. f(2)= h. f(-1)= [10 8 20. Determine the angle between a = (5, 3, 0) and b = (-1, 0, 8) 21. The vertices of a quadrilateral are A = [0,3,5], B = [-3,-1,17], C = [4,-3,15] & D = [7,1,3]. Prove that ABCD is a parallelogram. x-1 y-2 z+1 22. Determine the value of k for which the direction vectors of the lines || = and k 2 k-1 x+3 Ꮓ y = -1 are perpendicular. -2 1
33. Sketch the diagram that you would use to find the magnitude of the sum of a and b if the angle between them is 67° and the magnitudes are 7 and 11 respectively. Ensure that all vectors are labelled. Also include the equilibrium vector in your diagram. 34. For the function whose graph is given below, find the following: [ a. lim f(x)= x-2 b. lim f(x)= x-2° c. lim f(x)= x 2 d. lim f(x)= e. lim f(x)= x-1 f. lim f(x)= x1 g. f(2)= h. f(-1)= [10 8 20. Determine the angle between a = (5, 3, 0) and b = (-1, 0, 8) 21. The vertices of a quadrilateral are A = [0,3,5], B = [-3,-1,17], C = [4,-3,15] & D = [7,1,3]. Prove that ABCD is a parallelogram. x-1 y-2 z+1 22. Determine the value of k for which the direction vectors of the lines || = and k 2 k-1 x+3 Ꮓ y = -1 are perpendicular. -2 1
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
Transcribed Image Text:33. Sketch the diagram that you would use to find the magnitude of the sum of a and b if the angle between
them is 67° and the magnitudes are 7 and 11 respectively. Ensure that all vectors are labelled. Also
include the equilibrium vector in your diagram.
34. For the function whose graph is given below, find the following: [
a. lim f(x)=
x-2
b. lim f(x)=
x-2°
c.
lim f(x)=
x 2
d. lim f(x)=
e.
lim f(x)=
x-1
f. lim f(x)=
x1
g. f(2)=
h. f(-1)=
[10
8
![20. Determine the angle between a = (5, 3, 0) and b = (-1, 0, 8)
21. The vertices of a quadrilateral are A = [0,3,5], B = [-3,-1,17], C = [4,-3,15] & D = [7,1,3].
Prove that ABCD is a parallelogram.
x-1
y-2
z+1
22. Determine the value of k for which the direction vectors of the lines
||
=
and
k
2
k-1
x+3
Ꮓ
y = -1 are perpendicular.
-2
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F633dc666-1c4e-4222-82a0-1d910c7662c5%2F72ba5069-4252-46a2-9c36-81a7a3ed9678%2Frs0r48f_processed.png&w=3840&q=75)
Transcribed Image Text:20. Determine the angle between a = (5, 3, 0) and b = (-1, 0, 8)
21. The vertices of a quadrilateral are A = [0,3,5], B = [-3,-1,17], C = [4,-3,15] & D = [7,1,3].
Prove that ABCD is a parallelogram.
x-1
y-2
z+1
22. Determine the value of k for which the direction vectors of the lines
||
=
and
k
2
k-1
x+3
Ꮓ
y = -1 are perpendicular.
-2
1
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