Question

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.

Answer 1

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