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If `A(1,2,-3)` and `B(-1,-2,1)` are the two given points in space then find (i) the direction ratios of `vec(AB)` and (ii) the direction cosines of`vec(AB)`. Express `vec(AB)` in terms of `hati , hatj` and `hatk`. |
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Answer» (i) The direction ratios of `vec(AB)` are `(-1,-1),(-2,-2),(1+3)` , i.e, `-2,-4,4`. (ii) `|vec(AB)| = sqrt((-2)^(2) + (-4)^(2) + 4^(2)) = sqrt(36) = 6`. `:.` the direction cosines of `vec(AB)` are `(-2)/(6), (-4)/(4),4/6` i.e., `(-1)/(3),(-2)/(3), (2)/(3)`. Clearly, `vec(AB) = - 1/3 hati, - 2/3 hatj + 2/3 hatk`. |
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