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Question
If two sides of a triangle are `hat"i" + 2hat"j" and hat"i" + hat"k"`, find the length of the third side.
Solution
Let ABC be a triangle with `bar"AB" = hat"i" + 2hat"j", bar"BC" = hat"i" + hat"k"`.
By triangle law of vectors
`bar"AC" = bar"AB" + bar"BC"`
`= (hat"i" + 2hat"j") + (hat"i" + hat"k")`
`= 2hat"i" + 2hat"j" + hat"k"`
∴ l(AC) = `|bar"AC"| = sqrt(2^2 + 2^2 + 1^2) = sqrt9` = 3 units
Hence, the length of third side is 3 units.
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