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Check whether the vectors ijkijk2i^+2j^+3k^, -3i^+3j^+2k^ and ik3i^+4k^ form a triangle or not. - Mathematics and Statistics

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Sum

Check whether the vectors `2hat"i" + 2hat"j" + 3hat"k",  - 3hat"i" + 3hat"j" + 2hat"k"` and `3hat"i" + 4hat"k"` form a triangle or not.

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Solution

Let, if possible, the three vectors form a triangle ABC with `bar"AB" = 2hat"i" + 2hat"j" + 3hat"k"`,

`bar"BC" = - 3hat"i" + 3hat"j" + 2hat"k"`

`bar"AC" = 3hat"i" + 4hat"k"`

Now, `bar"AB" + bar"BC"`

`= (2hat"i" + 2hat"j" + 3hat"k") + (- 3hat"i" + 3hat"j" + 2hat"k")`

= `- hat"i" + 5hat"j" + 5hat"k"  ≠  3hat"i" + 4hat"k" = bar"AC"`

Hence, the three vectors do not form a triangle.

Concept: Vectors and Their Types
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