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If two sides of a triangle are hat"i" + 2hat"j" and hat"i" + hat"k", find the length of the third side. - Mathematics and Statistics

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Sum

If two sides of a triangle are `hat"i" + 2hat"j" and hat"i" + hat"k"`, find the length of the third side.

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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.

Concept: Vectors and Their Types
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