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A variable plane makes intercepts on x, y and z axes and it makes a tetrahedron of volume 64 cu. Units. The locus of foot of perpendicular from origin on the plane is |
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Answer» `(x^(2)+y^(2)+z^(2))^(2)=384 xyz` VOLUME of TETRAHEDRON OABC is `v=(abc)/6=64 rArr abc=384` Foot of perpendicular forrm (0,0,0) on this plane is `x/(1//a)=y/(1//b)=z/(1//c)=1/(1/a^(2) +1/b^(2)+1/c^(2))`=k `rArr x=k/a, y=k/b, z=k/c` and `1/k=1/a^(2)+1/b^(2)+1/c^(2)` `rArr 1/k=(x^(2)+y^(2)+z^(2))/k^(2) rArr x^(2)+y^(2)+z^(2)=`k `therefore (x^(2)+y^(2)+z^(2))^(2)=abc xyz=384 xyz` is the required locus. |
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