Find a vector that points in the same direction as the vector (i + j) and whose magnitude is 1.
Through the power of repeatedly guessing I found the answer to be ( .707i + .707j ) but theres got to be a legit way of finding those values rather than guessing. going through the steps will help me out a lot, thanks
Through the power of repeatedly guessing I found the answer to be ( .707i + .707j ) but theres got to be a legit way of finding those values rather than guessing. going through the steps will help me out a lot, thanks
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Because it's traveling in the direction (i+j), its velocity can expressed as (ai + aj) where a is a scalar constant.
The amplitude of (ai+aj) will be √(a²+a²) = a√2.
For magnitude 1, a√2 = 1
So a = 1/√2 = √(1/2) = 0.70710678...
The amplitude of (ai+aj) will be √(a²+a²) = a√2.
For magnitude 1, a√2 = 1
So a = 1/√2 = √(1/2) = 0.70710678...
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(1/sqrt(2)) i + (1/sqrt(2)) j
The reason for this is that you want the magnitude of the final vector to be 1 and the way that you find the magnitude of the vector v=ai+bj is Sqrt(v (dot) v) in this case that gives Sqrt(a^2+b^2) which gives Sqrt((1/2)+(1/2) =Sqrt(1)=1. The reason it can only be this answer is because a and b have to be equal so that the vector points in the same direction as (i+j).
The reason for this is that you want the magnitude of the final vector to be 1 and the way that you find the magnitude of the vector v=ai+bj is Sqrt(v (dot) v) in this case that gives Sqrt(a^2+b^2) which gives Sqrt((1/2)+(1/2) =Sqrt(1)=1. The reason it can only be this answer is because a and b have to be equal so that the vector points in the same direction as (i+j).