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Find the direction cosines of the vecto...

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

Text Solution

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Clearly, `AB=(-1-1)hati+(-2-2)hatj+(1+3)hatk=-2hati-4hatj+4hatk`
Now, `|AB|=sqrt((-2)^(2)+(-4)^(2)+(4)^(2))=sqrt(36)=6`
`therefore`Unit vector along `AB=(AB)/(|AB|)=(-2hati-4hatj+4hatk)/(6)`
`=-(1)/(3) hati-(2)/(3)hatj+(2)/(3) hatk`
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