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Let vector u=<1,-4>,vector v=<-2,-5>, and vector w=<-1,2>. Find the...
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You need to evaluate the lengths of the vectors `bar u, bar v, bar w` and `bar x` such that:
`|bar u| = sqrt(1^2 + (-4)^2) => |bar u| = sqrt 17`
`|bar v| = sqrt((-2)^2 + (-5)^2) => |bar v| = sqrt 29`
`|bar w| = sqrt ((-1)^2+2^2) => |bar w| = sqrt 5`
`|bar x| = sqrt(a^2 + b^2)`
The problem provides the information that `9(|u|)-(|v|)+(|x|) = 10(|x|)+(|w|)` , hence, you need to substitute the lengths evaluated above, such that:
`9sqrt17 - sqrt29 + sqrt(a^2 + b^2) = 10sqrt(a^2 + b^2) + sqrt 5`
You need to isolate the terms that contain `sqrt(a^2 + b^2)` to one side, such that:
`9sqrt(a^2 + b^2) = 9sqrt17 - sqrt29 - sqrt5`
Dividing by 9 both sides yields:
`sqrt(a^2 + b^2) = sqrt17 - sqrt29/9 - sqrt5/9`
Hence, evaluating the length of vector `bar x` , under the given conditions, yields `|bar x| = sqrt(a^2 + b^2) = sqrt17 - sqrt29/9 - sqrt5/9.`
Posted by sciencesolve on January 16, 2013 at 8:25 AM (Answer #1)
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