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If A and B are foot of perpendicular drawn from point Q(a,b,c) to the planes yz and zx, then equation of plane through the point A,B, and O isA. `(x)/(a)+(y)/(b)-(z)/(c)=0`B. `(x)/(a)-(y)/(b)+(z)/(c)=0`C. `(x)/(a)-(y)/(b)-(z)/(c)=0`D. `(x)/(a)+(y)/(b)+(z)/(c)=0` |
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Answer» Correct Answer - A The foot of perpendicular from point Q(a,b,c) to the yz plane is A(0,b,c) and the foot of perpendicular from point Q to the foot of perpendicular from point Q to zx plane in B(a, 0, c). Let the.equation of plane passing through the point (0, 0, 0) be Ax+By+Cz=0 ... (i) Also it is paring through the point A( 0, b, c) and B(a,0,c) `therefore 0+Bc+C c=0` `and Aa+0+C c=0` `Rightarrow C c=Bb` and `C c=-A a ` `therefore A=-(k)/(a), B=-(k)/(b)` and `C=(k)/(c)` From Eq. (i) , `(-k)/(a)x-(k)/(b)y+(k)/(c)z=0` `Rightarrow -(x)/(a)-(y)/(b)+(z)/(c)=0 or (x)/(a)+(y)/(b)+(z)/(c)=0` |
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