Math CentralQuandaries & 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


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.


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