A) \[5\]
B) \[5\sqrt{5}\]
C) \[10\sqrt{5}\]
D) None of these
Correct Answer: B
Solution :
Let \[l,\] \[m\] and \[n\] be the direction cosine?s of the given line segment PQ. \[\therefore \] \[l=\cos \,\alpha ,\,\,\,m=\cos \beta ,\,\,n=\cos \,\gamma \] where \[\alpha ,\beta ,\gamma \] are the angles which the line segment PQ makes with the axes. Suppose length of line segment \[PQ=r\] This, projection of line segment PQ on x-axis \[=PQ\,\,\cos \,\alpha =rl\] Also, the projection of line segment PQ on x-axis \[=8\] \[\therefore \] \[lr=8\] Similarly \[mr=5,\,\,nr=6\] Now, on squaring adding these equations, we get \[{{(lr)}^{2}}+{{(mr)}^{2}}+{{(nr)}^{2}}={{8}^{2}}+{{5}^{2}}+{{6}^{2}}\] \[{{r}^{2}}({{l}^{2}}+{{m}^{2}}+{{n}^{2}})=64+25+36\] \[(\because \,\,\,\,{{l}^{2}}+{{m}^{2}}+{{n}^{2}}=1)\] \[\Rightarrow \] \[{{r}^{2}}=125\] \[\Rightarrow \] \[r=5\sqrt{3}\]
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