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Find the centre and radius of the following spheres : $| \overrightarrow{r}-(\overrightarrow(2i)-\overrightarrow(j)+\overrightarrow{4k})|=5$

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  • Vector equation of a sphere with centre $ \overrightarrow c$ and radius $a$ is $|\overrightarrow r-\overrightarrow c|=a$ When the centre is at the origin, the vector equation is $|\overrightarrow r|=a$ Cartesian equation is $ (x-c_1)^2+(y-c_2)^2+(z-c_3)^2=a^2$ where $(c_1, c_2, c_3 )$ is the centre.
$|\overrightarrow r-(2\overrightarrow i-\overrightarrow j+4\overrightarrow k)|=5$ pv of centre $\overrightarrow c=2\overrightarrow i-\overrightarrow j+4\overrightarrow k$ i.e., $c(2, -1, 4)$ and radius 5.
answered Jun 18, 2013 by thanvigandhi_1

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