A) \[\sqrt{10}\]
B) \[\sqrt{7}\]
C) \[\sqrt{5}\]
D) \[1\]
Correct Answer: A
Solution :
The equation of line which passes through the point A (4,2,2) and parallel to the vector \[2\hat{i}+3\hat{j}+6\hat{k}\]is \[\frac{x-4}{2}=\frac{y-2}{3}=\frac{z-2}{6}\] Distance of point P from the line \[=\sqrt{\Sigma {{({{x}_{1}}-{{x}_{2}})}^{2}}-{{(\Sigma l({{x}_{1}}-{{x}_{2}}))}^{2}}}\] \[=\sqrt{\begin{align} & {{(1-4)}^{2}}+{{(2-2)}^{2}}+{{(3-2)}^{2}}-\{2(1-4) \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+3(2-2)+6(3-2){{\}}^{2}} \\ \end{align}}\] \[=\sqrt{9+0+1-{{(-6+0+6)}^{2}}}=\sqrt{10}\]
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