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Statement 1: Let A,B,C be the image of point P(a,b,c) in YZ,ZX andXY planes respectively. Then, the equation of the plane passing through points A,B,C cuts intercepts a,b,c on the coordinate axes.Statement 2: The image (alpha, beta, gamma) of a point (x_(1),y_(1),z_(1)) in the plane ax+by+cz+d=0 is given by(alpha-x_(1))/a=(beta-y_(1))/b=(gamma-z_(1))/c=-(2(ax_(1)+by_(1)+cz_(1)+d))/(a^(2)+b^(2)+c^(2)) |
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Answer» STATEMENT-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1. Using statement 2 the image of POINT `P(a,b,c)` in `yz,zx` and `xy` planes are `A(-a,b,c),B(a,-b,c)` and `C(a,b,-c)` respectively. LET the equation of the plane passing through `(a-,b,c)` be `U(x+a)+V(y-b)+W(z-c)=0`..............i It passes through `(a,-b,c)` and `(a,b,-c)` `:. 2Ua-2Vb=0W=0` `2Ua+0V-2Wc=0` `impliesU/(4bc)=V/(4ac)=W/(4ab)` Substituting the values `U,V,W ` in (i)we OBTAIN `bc(x+a)+ca(y-b)+ab(z-c)=0impliesx/a+y/b+z/c=1` Clearly, this plane cuts intercepts a,b and c on the coordinate axes. |
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