I understand how to solve this problem: i.e. take the unit vector of a, then multiply by our given magnitude (in this case sqrt2) which gives: (sqrt2)/(5)(3i+4j). I'm confused as to what the mathematical logic behind this, how would you explain why we're doing this process?

hotonglamoz 2022-09-22 Answered
I understand how to solve this problem: i.e. take the unit vector of a, then multiply by our given magnitude (in this case 2 ) which gives: 2 5 ( 3 i + 4 j )
I'm confused as to what the mathematical logic behind this, how would you explain why we're doing this process?
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Answers (2)

Kody Gates
Answered 2022-09-23 Author has 5 answers
Magnitude of b = i j | b | = 1 2 + ( 1 ) 2 = 2
Unit vector parallel to a = 3 i + 4 j a ^ = a | a | = 3 i + 4 j 3 2 + 4 2 = 1 5 ( 3 i + 4 j )
The required vector with magnitude equal to that of b & directed along a :
| b | a ^ = 2 1 5 ( 3 i + 4 j ) = 2 5 ( 3 i + 4 j )
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Hagman7v
Answered 2022-09-24 Author has 3 answers
The solution that you mentiond was this: b a a = b a a. Since it is a times a positive number, it has the same direction as a. Besides,
b a a = b a a = b ,
as you wanted.
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