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Question
Find the direction cosines of the vector joining the points A (1, 2, -3) and B (-1, -2, 1) directed from A to B.
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Solution
The given points are A (1, 2, -3) and B (-1, -2, 1).
`therefore vec(AB) = (- hati -2hatj + hatk) - (hati + 2hatj - 3hatk)`
`= -2hati - 4hatj + 4hatk`
⇒ `vec(AB) = -2hati - 4hatj + 4hatk`
`therefore |vec(AB)| = sqrt((-2)^2 + (-4)^2 + 4^2) `
`= sqrt(4 + 16 + 16) `
`= sqrt36 = 6`
∴ Hence, the direction cosines of `vec(AB)` are `((-2)/6, (-4)/6, 4/6) = ((-1)/3. (-2)/3, 2/3)`.
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