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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?
- ?Lv 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.
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- Daniel HLv 51 month ago
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⟩