121373 Let the plane \(2 x+3 y+z+20=0\) be rotated through a right angle about its line of intersection with the plane \(x-3 y+5 z=8\). If the mirror image of the point \(\left(2,-\frac{1}{2}, 2\right)\) in the rotated plane is \(B(a, b, c)\), then:

121374 Let two vertices of triangle \(A B C\) be \((2,4,6)\) and \((0,-2,-5)\), and its centroid be \((2,1,-1)\). If the image of third vertex in the plane \(x+2 y+4 z=\) 11 is \((\alpha, \beta, \gamma)\), then \(\alpha \beta+\beta \gamma+\gamma \alpha\) is equal to

121376 Let \(P\) be the plane containing the straight line \(\frac{x-3}{9}=\frac{y+4}{-1}=\frac{z-7}{3}\) and perpendicular to the plane containing the straight lines \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\) and \(\frac{x}{3}=\frac{y}{7}=\frac{z}{8}\). If \(d\) is the distance of \(P\) from the point \((2,-5,11)\), then \(\mathrm{d}^2\) is equal to :

121377 Let \(Q\) be the mirror image of the point \(P(1,0,1)\) with respect to the plane \(S: x+y+z=5\). If a line \(L\) passing through \((1,-1,-1)\), parallel to the line \(P Q\) meets the plane \(S\) at \(R\), then \(Q R^2\) is equal to:

121373 Let the plane \(2 x+3 y+z+20=0\) be rotated through a right angle about its line of intersection with the plane \(x-3 y+5 z=8\). If the mirror image of the point \(\left(2,-\frac{1}{2}, 2\right)\) in the rotated plane is \(B(a, b, c)\), then:

121374 Let two vertices of triangle \(A B C\) be \((2,4,6)\) and \((0,-2,-5)\), and its centroid be \((2,1,-1)\). If the image of third vertex in the plane \(x+2 y+4 z=\) 11 is \((\alpha, \beta, \gamma)\), then \(\alpha \beta+\beta \gamma+\gamma \alpha\) is equal to

121376 Let \(P\) be the plane containing the straight line \(\frac{x-3}{9}=\frac{y+4}{-1}=\frac{z-7}{3}\) and perpendicular to the plane containing the straight lines \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\) and \(\frac{x}{3}=\frac{y}{7}=\frac{z}{8}\). If \(d\) is the distance of \(P\) from the point \((2,-5,11)\), then \(\mathrm{d}^2\) is equal to :

121377 Let \(Q\) be the mirror image of the point \(P(1,0,1)\) with respect to the plane \(S: x+y+z=5\). If a line \(L\) passing through \((1,-1,-1)\), parallel to the line \(P Q\) meets the plane \(S\) at \(R\), then \(Q R^2\) is equal to:

121373 Let the plane \(2 x+3 y+z+20=0\) be rotated through a right angle about its line of intersection with the plane \(x-3 y+5 z=8\). If the mirror image of the point \(\left(2,-\frac{1}{2}, 2\right)\) in the rotated plane is \(B(a, b, c)\), then:

121374 Let two vertices of triangle \(A B C\) be \((2,4,6)\) and \((0,-2,-5)\), and its centroid be \((2,1,-1)\). If the image of third vertex in the plane \(x+2 y+4 z=\) 11 is \((\alpha, \beta, \gamma)\), then \(\alpha \beta+\beta \gamma+\gamma \alpha\) is equal to

121376 Let \(P\) be the plane containing the straight line \(\frac{x-3}{9}=\frac{y+4}{-1}=\frac{z-7}{3}\) and perpendicular to the plane containing the straight lines \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\) and \(\frac{x}{3}=\frac{y}{7}=\frac{z}{8}\). If \(d\) is the distance of \(P\) from the point \((2,-5,11)\), then \(\mathrm{d}^2\) is equal to :

121377 Let \(Q\) be the mirror image of the point \(P(1,0,1)\) with respect to the plane \(S: x+y+z=5\). If a line \(L\) passing through \((1,-1,-1)\), parallel to the line \(P Q\) meets the plane \(S\) at \(R\), then \(Q R^2\) is equal to:

121373 Let the plane \(2 x+3 y+z+20=0\) be rotated through a right angle about its line of intersection with the plane \(x-3 y+5 z=8\). If the mirror image of the point \(\left(2,-\frac{1}{2}, 2\right)\) in the rotated plane is \(B(a, b, c)\), then:

121374 Let two vertices of triangle \(A B C\) be \((2,4,6)\) and \((0,-2,-5)\), and its centroid be \((2,1,-1)\). If the image of third vertex in the plane \(x+2 y+4 z=\) 11 is \((\alpha, \beta, \gamma)\), then \(\alpha \beta+\beta \gamma+\gamma \alpha\) is equal to

121376 Let \(P\) be the plane containing the straight line \(\frac{x-3}{9}=\frac{y+4}{-1}=\frac{z-7}{3}\) and perpendicular to the plane containing the straight lines \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\) and \(\frac{x}{3}=\frac{y}{7}=\frac{z}{8}\). If \(d\) is the distance of \(P\) from the point \((2,-5,11)\), then \(\mathrm{d}^2\) is equal to :

121377 Let \(Q\) be the mirror image of the point \(P(1,0,1)\) with respect to the plane \(S: x+y+z=5\). If a line \(L\) passing through \((1,-1,-1)\), parallel to the line \(P Q\) meets the plane \(S\) at \(R\), then \(Q R^2\) is equal to: