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Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# 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

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• rotchm
Lv 7
1 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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• 1 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⟩

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