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anonymous
 5 years ago
Find all vector < 1, a, b> orthogonal to <4, 8, 2>.
This is what I got so far, but I'm not sure whether my process is correct or not.
let u = < 1, a, b> and v = <4, 8, 2>.
u*v = < 1, a, b> *<4, 8, 2>= 48a+2b
set 48a+2b= 0
anonymous
 5 years ago
Find all vector < 1, a, b> orthogonal to <4, 8, 2>. This is what I got so far, but I'm not sure whether my process is correct or not. let u = < 1, a, b> and v = <4, 8, 2>. u*v = < 1, a, b> *<4, 8, 2>= 48a+2b set 48a+2b= 0

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Your process if correct assuming you're using the dot product definition :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes by dot product definition. u*v=0 which orthogonal, but how do I do it? I stuck with solve a and b. For some reason, I keep getting 0 = 0.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh, well, you have one equation in two unknowns, so technically, you have an infinite number of solutions. You can see it clearer if you say, set a=t. Then\[48a+2t \rightarrow b=4t2\]Then the set of all vectors orthogonal to <4,8,2> is\[\left\{ <1,a,b>t \in \mathbb{R}, a=t, b=4t2 \right\}\]That is,\[<1,t,4t2>\]where t is any real number. You could have chosen b=t and solved for a, or even just solve b for a or a for b. For example, since \[48a+2b=0 \rightarrow b=4a2\]and you could just write,\[<1,a,4a2>\]where a is real. The point is, when you more unknowns than equations, you will have an infinite number of solutions. Check with a couple of numerical examples if you like.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Example: Find two vectors orthogonal to <4,8,2>. Taking your set of possible vectors, <1,a,4a2>, let a=0 for one, and let a=1 for the other (you can pick any real number, I just picked these for ease). Then two possible orthogonal vectors are: <1,0,2> and <1,1,2>. We can check: <4,8,2>.<1,0,2> = 4 + 0  4 = 0 ... good. <4,8,2>.<1,1,2> = 4  8 + 4 = 0 ... good. This is how it works. Hope it helps :)
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