B) Prove that: 1) 2) a L2: Q2] A) Find the angles (a,0) between the following planes e || PLI: -2x+y-z=3 44 PL2: x+3y+z=4 a. (bx c) = c.(ax 5) for any three vectors a, b, c 4s L(cos 0.5 t) = (use the basic definition of lanlagr
B) Prove that: 1) 2) a L2: Q2] A) Find the angles (a,0) between the following planes e || PLI: -2x+y-z=3 44 PL2: x+3y+z=4 a. (bx c) = c.(ax 5) for any three vectors a, b, c 4s L(cos 0.5 t) = (use the basic definition of lanlagr
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![B) Prove that:
1)
2)
Q2] A) Find the angles (a,0) between the following planes
2√√
α
+2
Majid
Examiner
L1:
Ꮎ
t
2) f(t) = sin
t
L2:
5-x
-3
1+x
9
y-2 2+z
-1 3
3-2
-3
=
a. (bx c) = c.(axb) for any three vectors a, b, c
(use the basic definition of laplace transformation)
4s
L(cos 0.5 t)
4s²+1
Q3] Find inverse laplace transform of:
TC
0.2s e 3
1)
2s²+6
6
s²-4s+13
2)
Q4] All points of plane PL are equidistance from point (2,-1,1) and (3,1,5), find equation of
PL
PL1: -2x+y-z=3
PL2: x+3y+z=4
Q5] Find laplase transform for the following functions:
1)
Periodic functin f(t) where:
t
for 0≤t≤a
f(t) = {2- t/a for a< t < 2α-
5.
((Good Luck))
Mofendersid
Head of the Department](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a68099d-a123-43b1-bb38-8c309d9a0055%2F470e45a1-19d3-44ec-b935-a7bcc6e35f10%2Fe4n3jts_processed.jpeg&w=3840&q=75)
Transcribed Image Text:B) Prove that:
1)
2)
Q2] A) Find the angles (a,0) between the following planes
2√√
α
+2
Majid
Examiner
L1:
Ꮎ
t
2) f(t) = sin
t
L2:
5-x
-3
1+x
9
y-2 2+z
-1 3
3-2
-3
=
a. (bx c) = c.(axb) for any three vectors a, b, c
(use the basic definition of laplace transformation)
4s
L(cos 0.5 t)
4s²+1
Q3] Find inverse laplace transform of:
TC
0.2s e 3
1)
2s²+6
6
s²-4s+13
2)
Q4] All points of plane PL are equidistance from point (2,-1,1) and (3,1,5), find equation of
PL
PL1: -2x+y-z=3
PL2: x+3y+z=4
Q5] Find laplase transform for the following functions:
1)
Periodic functin f(t) where:
t
for 0≤t≤a
f(t) = {2- t/a for a< t < 2α-
5.
((Good Luck))
Mofendersid
Head of the Department
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