Question

If A = (1, 1, -1), B = (3,-1, 2), then the direction cosines of line AB are​

Answer 1

${\huge{\fcolorbox{black}{white}{\fcolorbox{black}{lightyellow}{\bf{\color{black}{ANSWER}}}}}}$

$&#10148$ A = (1,1,-1) B=(3,-1,2)

so the vector line AB = (3-1),(-1-1),(2+1) = (2,-2,3)

magnitude of line AB

$&#10230 \: \: \sqrt{ {(2)}^{2} + { (- 2)}^{2} + {(3)}^{2} } \\ \\ &#10230 \: \: \sqrt{4 + 4 + 9} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ &#10230 \: \: \sqrt{17} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Now the direction of cosines of line AB

$&#10230 \: \: (\frac{2}{ \sqrt{17} } \frac{ - 2}{ \sqrt{17} } \frac{3}{ \sqrt{17} } )$