121415 A plane meets the co-ordinate axes at the points \(A, B, C\) respectively in such a way that the centric of \(\triangle A B C\) is \(\left(1, r, r^2\right)\) for some real \(r\). If the plane passes through the point \((5,5,-12)\) then \(\mathrm{r}=\)

121416 The distance of the point \((-2,4,-5)\) from the line \(\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}\) is

121418 The point of intersection of the lines \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) and \(\frac{x-4}{5}=\frac{y-1}{2}=z\), is

121420 \(A B\) and \(C D\) are 2 line segments, where \(A(2,3\), \(0), B(6,9,0), C(-6,-9,0)\). \(P\) and \(Q\) are midpoint of \(A B\) and \(C D\), respectively and \(L\) is the midpoint of \(P Q\). Find the distance of \(L\) from the plane \(3 x+4 z+25=0\).

121422 The length of the perpendicular from the point \((1,-2,5)\) on the line passing through \((1,2,4)\) and parallel to the line \(x+y-z=0\) and \(x-2 y\) \(+3 \mathrm{z}-5\) is

121415 A plane meets the co-ordinate axes at the points \(A, B, C\) respectively in such a way that the centric of \(\triangle A B C\) is \(\left(1, r, r^2\right)\) for some real \(r\). If the plane passes through the point \((5,5,-12)\) then \(\mathrm{r}=\)

121416 The distance of the point \((-2,4,-5)\) from the line \(\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}\) is

121418 The point of intersection of the lines \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) and \(\frac{x-4}{5}=\frac{y-1}{2}=z\), is

121420 \(A B\) and \(C D\) are 2 line segments, where \(A(2,3\), \(0), B(6,9,0), C(-6,-9,0)\). \(P\) and \(Q\) are midpoint of \(A B\) and \(C D\), respectively and \(L\) is the midpoint of \(P Q\). Find the distance of \(L\) from the plane \(3 x+4 z+25=0\).

121422 The length of the perpendicular from the point \((1,-2,5)\) on the line passing through \((1,2,4)\) and parallel to the line \(x+y-z=0\) and \(x-2 y\) \(+3 \mathrm{z}-5\) is

121415 A plane meets the co-ordinate axes at the points \(A, B, C\) respectively in such a way that the centric of \(\triangle A B C\) is \(\left(1, r, r^2\right)\) for some real \(r\). If the plane passes through the point \((5,5,-12)\) then \(\mathrm{r}=\)

121416 The distance of the point \((-2,4,-5)\) from the line \(\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}\) is

121418 The point of intersection of the lines \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) and \(\frac{x-4}{5}=\frac{y-1}{2}=z\), is

121420 \(A B\) and \(C D\) are 2 line segments, where \(A(2,3\), \(0), B(6,9,0), C(-6,-9,0)\). \(P\) and \(Q\) are midpoint of \(A B\) and \(C D\), respectively and \(L\) is the midpoint of \(P Q\). Find the distance of \(L\) from the plane \(3 x+4 z+25=0\).

121422 The length of the perpendicular from the point \((1,-2,5)\) on the line passing through \((1,2,4)\) and parallel to the line \(x+y-z=0\) and \(x-2 y\) \(+3 \mathrm{z}-5\) is

121415 A plane meets the co-ordinate axes at the points \(A, B, C\) respectively in such a way that the centric of \(\triangle A B C\) is \(\left(1, r, r^2\right)\) for some real \(r\). If the plane passes through the point \((5,5,-12)\) then \(\mathrm{r}=\)

121416 The distance of the point \((-2,4,-5)\) from the line \(\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}\) is

121418 The point of intersection of the lines \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) and \(\frac{x-4}{5}=\frac{y-1}{2}=z\), is

121420 \(A B\) and \(C D\) are 2 line segments, where \(A(2,3\), \(0), B(6,9,0), C(-6,-9,0)\). \(P\) and \(Q\) are midpoint of \(A B\) and \(C D\), respectively and \(L\) is the midpoint of \(P Q\). Find the distance of \(L\) from the plane \(3 x+4 z+25=0\).

121422 The length of the perpendicular from the point \((1,-2,5)\) on the line passing through \((1,2,4)\) and parallel to the line \(x+y-z=0\) and \(x-2 y\) \(+3 \mathrm{z}-5\) is

121415 A plane meets the co-ordinate axes at the points \(A, B, C\) respectively in such a way that the centric of \(\triangle A B C\) is \(\left(1, r, r^2\right)\) for some real \(r\). If the plane passes through the point \((5,5,-12)\) then \(\mathrm{r}=\)

121416 The distance of the point \((-2,4,-5)\) from the line \(\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}\) is

121418 The point of intersection of the lines \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) and \(\frac{x-4}{5}=\frac{y-1}{2}=z\), is

121420 \(A B\) and \(C D\) are 2 line segments, where \(A(2,3\), \(0), B(6,9,0), C(-6,-9,0)\). \(P\) and \(Q\) are midpoint of \(A B\) and \(C D\), respectively and \(L\) is the midpoint of \(P Q\). Find the distance of \(L\) from the plane \(3 x+4 z+25=0\).

121422 The length of the perpendicular from the point \((1,-2,5)\) on the line passing through \((1,2,4)\) and parallel to the line \(x+y-z=0\) and \(x-2 y\) \(+3 \mathrm{z}-5\) is