The length of a vector - Math Central

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Quandaries & Queries

Question from kyrie, a student:

Find the possible values of the constant a such that
| ai + 4aj + 4k | = 13
I know the answer is 3 but not sure how to get to it

Kyrie,

The length of a vector pi + qj + rk is designated |pi + qj + rk| and is given by the expression

|pi + qj + rk| = √(p² + q² + r²).

For your vector this means that

√(a² + (4a)² + 4²) = 13

Solve for a.

Penny

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