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anonymous
 4 years ago
consider the vector I =[ 1/Square root (2) , 1/Square root (2)] and J= [ 1/Square root (2), 1/Square root (2)]. Write the vector (2,6) in terms of I and J.
anonymous
 4 years ago
consider the vector I =[ 1/Square root (2) , 1/Square root (2)] and J= [ 1/Square root (2), 1/Square root (2)]. Write the vector (2,6) in terms of I and J.

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phi
 4 years ago
Best ResponseYou've already chosen the best response.3james gave you a good starting point. I= [1 1]/sqrt(2) J= [1 1]/sqrt(2) you want to find two scalars (two simple numbers) that you multiply I and J by to get (2,6) call the numbers a and b then you must solve (2,6)= a*I + b*J

phi
 4 years ago
Best ResponseYou've already chosen the best response.3First rule: multiplying a vector by a scalar uses this rule: a (x,y)= (ax, ay)

phi
 4 years ago
Best ResponseYou've already chosen the best response.3so, start with (2,6)= a*I + b*J (2, 6) = a*(1,1)/sqrt(2) + b*(1,1)/sqrt(2) multiply both sides by sqrt(2) . This means multiply every term by sqrt(2) you get sqrt(2) * (2, 6) = a*(1,1) + b*(1,1)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0hmm this one doesn't make sense to me at all

phi
 4 years ago
Best ResponseYou've already chosen the best response.3Now use the rule First rule: multiplying a vector by a scalar uses this rule: a (x,y)= (ax, ay) on all the terms

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so its 2 sqrt(2) , 6 sqrt(2) = a (1,1) + b (1,1)

phi
 4 years ago
Best ResponseYou've already chosen the best response.3yes, but apply the rule to the two terms on the right hand side also

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so its 2sqrt(2) , 6sqrt(2) = (a1, a1) + (b, b1)

phi
 4 years ago
Best ResponseYou've already chosen the best response.3well, I would not write a1, because a*1 is just a.... also, put the left side in parens because we do not want to forget is is a vector

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok. its [2sqrt(2), 6sqrt(2)] = (a,a) + (b,b) ?

phi
 4 years ago
Best ResponseYou've already chosen the best response.3yes, now add the two vectors on the right hand side

phi
 4 years ago
Best ResponseYou've already chosen the best response.3You were able to subtract two vectors, for example PQ in the last problem. Adding is the same, except you add instead of subtract.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so its like (1+1, 1+1) = (0,2) ?

phi
 4 years ago
Best ResponseYou've already chosen the best response.3yes, but now we are adding variables instead of numbers

phi
 4 years ago
Best ResponseYou've already chosen the best response.3(a,a) + (b,b) = ?? add corresponding entries

phi
 4 years ago
Best ResponseYou've already chosen the best response.3yes, but normally you would write a + b as just ab .

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh ok. now what do i do?

phi
 4 years ago
Best ResponseYou've already chosen the best response.3You have (2sqrt(2), 6sqrt(2)) = (ab, a+b)

phi
 4 years ago
Best ResponseYou've already chosen the best response.3this means you have two vectors that equal each other. If they equal each other, what does that mean about each entry in the vector?

phi
 4 years ago
Best ResponseYou've already chosen the best response.3if I told you ( 1, 2) = (x, y) what is x and what is y how do you know?

phi
 4 years ago
Best ResponseYou've already chosen the best response.3Now use the same idea on our problem (2sqrt(2), 6sqrt(2)) = (ab, a+b)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0that ab = 2sqrt(2) and a+b = 6sqrt(2)

phi
 4 years ago
Best ResponseYou've already chosen the best response.3yes. we have 2 equations and two unknowns. The way to solve these types of equations is write them down like this: ab = 2sqrt(2) a+b = 6sqrt(2) add the two equations together (we are adding equal things to equal things, so the sum of them is still equal things) 2ab+b= 2sqrt(2)6sqrt(2) can you solve for a?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0would it be a = 2sqrt(2) 6sqrt(2) / 2 ??

phi
 4 years ago
Best ResponseYou've already chosen the best response.3first, you should put parens around (2sqrt(2) 6sqrt(2)) because you are dividing *both* terms by 2 (you divide the whole right hand side by 2) next, you should simplify

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so its [sqrt(2), 3sqrt(2)]?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh sqrt(2)i , 3sqrt(2) j

phi
 4 years ago
Best ResponseYou've already chosen the best response.3no. I mean you start with (2*sqrt(2)6*sqrt(2))/2 which is just a (ugly) number: divide both terms by 2 to get (sqrt(2)3*sqrt(2)) factor out sqrt(2) to get (13)*sqrt(2) simplify 13 to get a= 2*sqrt(2)

phi
 4 years ago
Best ResponseYou've already chosen the best response.3btw, if you want info on how to solve simultaneous equations like this one, watch http://www.khanacademy.org/video/solvingsystemsbyelimination?topic=workedexamples4 and his other examples

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0but what would be the answer for this?

phi
 4 years ago
Best ResponseYou've already chosen the best response.3we are getting there.... use a+b = 6sqrt(2) plus your value for a that we just found to get b

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so b = 6sqrt(2)  2sqrt(2) ?

phi
 4 years ago
Best ResponseYou've already chosen the best response.3well let's check that a + b= 6sqrt(2) 2*sqrt(2) + b= 6sqrt(2) add +2sqrt(2) to both sides to get b = 6sqrt(2)+2sqrt(2) so close, but not exactly correct. can you simplify this?

phi
 4 years ago
Best ResponseYou've already chosen the best response.3can you simplify b = 6sqrt(2)+2sqrt(2)

phi
 4 years ago
Best ResponseYou've already chosen the best response.3we have to answer Write the vector (2,6) in terms of I and J. which we decided meant: (2,6)= a*I + b*J we now know a and b, so the final answer is?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.02sqrt(2) i + 4sqrt(2) j ?

phi
 4 years ago
Best ResponseYou've already chosen the best response.3and what is I and J ? It does not hurt to write out the whole solution

phi
 4 years ago
Best ResponseYou've already chosen the best response.3I =[ 1/Square root (2) , 1/Square root (2)] J= [ 1/Square root (2), 1/Square root (2)] [2,6]=2sqrt(2) I + 4sqrt(2) J

phi
 4 years ago
Best ResponseYou've already chosen the best response.3You can check your answer by multiplying the scalars times the vectors, and then adding the vectors to see if you get [2, 6] btw, if you have time, you might want to brush up on your algebra using http://www.khanacademy.org/#corealgebra
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