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Question
Check whether the vectors `2hati + 2hatj + 3hatk, - 3hati + 3hatj + 2hatk` and `3hati + 4hatk` form a triangle or not.
Solution
Let, if possible, the three vectors form a triangle ABC with `barA = 2hati + 2hatj + 3hatk, barB = - 3hati + 3hatj + 2hatk, barC = 3hati + 4hatk`.
Now, `barA + barB`
= `(2hati + 2hatj + 3hatk) + (- 3hati + 3hatj + 2hatk)`
= `(2hati - 3hati) + (2hatj + 3hatj) + (3hatk + 2hatk)`
= `- hati + 5hatj + 5hatk ≠ 3hati + 4hatk`
`barA + barB ≠ barC`
Hence, the three vectors do not form a triangle.
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