Find the direction cosines of the vector joining the points A(1, 2,3) and B(-1, -2, 1) directed from A to B.

Explanation

The given points are `A(1, 2, -3) and B(-1, -2, 1)`.
Therefore,
`" "vec(AB)=(-1-1)hati+(-2-2)hatj+{1-(-3)}hatk`
`" "=-2hati-4hatj+4hatk`
`therfore" "|vec(AB)|=sqrt((-2)^(2)+(-4)^(2) + 4^(2)) =sqrt(4+ 16 +16) `
`" "=sqrt(36) = 6`
Hence, the direction cosines of `vec(AB)` are
`" "(-(2)/(6), -(4)/(6), (4)/(6))=(-(1)/(3), -(2)/(3), (2)/(3))`.