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# Consider the vectors: u = ⟨−2,a,1⟩ and v = ⟨4,0,b⟩ where a and b are positive numbers. Find a and b if ||u-v||=sqrt(61), and ||v||=5?

### 2 Answers

- rotchmLv 71 month ago
Hint: First, evaluate ||b||. This is something you should be able to do since it's basically something we learned in early high school. It's nothing new.

Once you've answered, then we will take it from there if need be.

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- Daniel HLv 51 month ago
1st v

sqrt(4^2 + 0^2 + b^2) = 5

4^2 + b^2 = 25

b = 3

u = <-2, a, 1>

v = <4, 0, 5>

u-v = <-6, a, 4>

sqrt((-6)^2 + a^2 + 4^2) = sqrt(61)

(-6)^2 + a^2 + 4^2 = 61

36 + a^2 + 16 = 61

a^2 = 9

a = +/- 3

u = ⟨−2, +/- 3, 1⟩ and v = ⟨4, 0, 5⟩