Answer to Question #298778 in Analytic Geometry for peter

Question #298778

If the position vector of A and B are 3 −→a − 7 −→b − 7 −→c and 5 −→a + 4 −→b + 3−→c , nd −→AB and determine its magnitude and direction cosines.


1
Expert's answer
2022-02-17T15:41:55-0500
AB=5a+4b+3c(3a7b7c)\overrightarrow{AB}=5\vec a+4\vec b+3\vec c-(3\vec a-7\vec b-7\vec c)

=2a+11b+10c=2\vec a+11\vec b+10\vec c

AB=22+112+102=15|\overrightarrow{AB}|=\sqrt{2^2+11^2+10^2}=15


cosα=215\cos \alpha=\dfrac{2}{15}

cosβ=1115\cos \beta=\dfrac{11}{15}

cosγ=1015\cos \gamma=\dfrac{10}{15}



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