Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
#1 2005-09-07 14:03:24
- Mukmin
- Guest
Simple Dot Product Question.. Please help, studying for quiz.
How do you solve this:
If a.b = 3, a.c = -1, and |a| = 2
what is a.(a+3b+7c)? I couldn't find "a" no matter what way i try it. The only way i could think of is
by setting a/|a| = 1
#2 2005-09-07 22:12:33
- Atled
- Member
- Registered: 2005-08-22
- Posts: 9
Re: Simple Dot Product Question.. Please help, studying for quiz.
A . (A + 3B +7C) = A.A + 3(A.B) + 7(A.C)
A.B and A.C are given
A . (A + 3B +7C) = A.A +(3*3) +(7*-1)
A . (A + 3B +7C) = A.A + 2
whats A.A
X.Y = |X|*|Y| * cos(θ)
A is PARALLEL to A there for θ = 0
or
The angle between A and A is 0
cos(0) = 1
A.A = 4
A . (A + 3B +7C) = 4 + 2 =6
hope that helps
edit: previously i said normal
Last edited by Atled (2005-09-09 12:52:58)
Offline
#3 2005-09-07 22:21:52
- MathsIsFun
- Administrator
- Registered: 2005-01-21
- Posts: 7,711
Re: Simple Dot Product Question.. Please help, studying for quiz.
(Atled - great post again - tell us more about yourself!)
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
Offline
#4 2005-09-08 00:59:49
- almukmin
- Member
- Registered: 2005-09-07
- Posts: 2
Re: Simple Dot Product Question.. Please help, studying for quiz.
A . (A + 3B +7C) = A.A + 3(A.B) + 7(A.C)
A.B and A.C are given
A . (A + 3B +7C) = A.A +(3*3) +(7*-1)
A . (A + 3B +7C) = A.A + 2
whats A.A
X.Y = |X|*|Y| * cos(θ)
A is normal to A there for θ = 0
or
The angle between A and A is 0
cos(0) = 1
A.A = 4
A . (A + 3B +7C) = 4 + 2 =6
hope that helps
I don't understand how come A.A is 4. Is |A| = A? What logic do u use to assume them equal? Thanks.
Offline
#5 2005-09-08 09:17:22
- MathsIsFun
- Administrator
- Registered: 2005-01-21
- Posts: 7,711
Re: Simple Dot Product Question.. Please help, studying for quiz.
So long ago since I did dot or cross products, but I may venture an answer:
Dot Product: X.Y = |X|*|Y| * cos(θ)
So: A.A = |A|*|A| * cos(θ) = |A|*|A| * 1 (because θ=0, ie there is a 0 angle between A and A) = 2*2 = 4
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
Offline
#6 2005-09-08 10:19:40
- almukmin
- Member
- Registered: 2005-09-07
- Posts: 2
Re: Simple Dot Product Question.. Please help, studying for quiz.
I just got an answer from my teacher. a.a is basically |a|^2
Offline
#7 2005-09-09 12:54:40
- Atled
- Member
- Registered: 2005-08-22
- Posts: 9
Re: Simple Dot Product Question.. Please help, studying for quiz.
About myself...
25/m/Ca
EE student at UC Davis
hobbies: cycling, skating, surfing although there are no oceans near davis 
Offline