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प्रश्न
If `4hati - 5hatj + hatk, 2hati + 3hatj + 3hatk` and `xhati + yhatj + zhatk` represent the sides AB, BC and AC respectively of a triangle ABC, then find x, y, z.
योग
उत्तर
We have by vector addition
`bar(AB) + bar(BC) = bar(AC)`
∴ `(4hati - 5hatj + hatk) + (2hati + 3hatj + 3hatk) = xhati + yhatj + zhatk`
∴ `6hati - 2hatj + 4hatk = xhati + yhatj + zhatk`
Comparing the coefficient of `hati, hatj, hatk` on both sides,
x = 6, y = –2, z = 4
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