121275 In three dimensional space \(x^2-5 x+6=0\) represents

121276 If the equation of the plane passing through the line of intersection of the planes \(2 x-y+z=3\), \(4 x-3 y+5 z+9=0\) and parallel to the line \(\frac{x+1}{-2}=\frac{y+3}{4}=\frac{z-2}{5}\) is \(a x+b y+c z+6=0\). Then \(\mathbf{a}+\mathbf{b}+\mathbf{c}\) is equal to

121277 A plane \(x\) passes through the point \((1,1,1)\). If \(b, c\), a are the direction ratios of a normal to the plane, where \(\mathbf{a}, \mathbf{b}, \mathbf{c}(\mathbf{a}\lt \mathbf{b}\lt \mathbf{c})\) are the factors of 2001,then the equation of the plane is

121279 If the plane \(56 x+4 y+9 z=2016\) meets the coordinated axes in \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) then the centroid of the triangle \(\mathrm{ABC}\) is

121280 The plane \(3 x+4 y+6 z+7=0\) is rotated about the line \(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}-\mathbf{3} \hat{\mathbf{k}})+(\mathbf{2} \hat{\mathbf{i}}-\mathbf{3} \hat{\mathbf{j}}+\hat{\mathbf{k}})\) unit the plane passes through origin. The equation of the plane in the new position is

121275 In three dimensional space \(x^2-5 x+6=0\) represents

121276 If the equation of the plane passing through the line of intersection of the planes \(2 x-y+z=3\), \(4 x-3 y+5 z+9=0\) and parallel to the line \(\frac{x+1}{-2}=\frac{y+3}{4}=\frac{z-2}{5}\) is \(a x+b y+c z+6=0\). Then \(\mathbf{a}+\mathbf{b}+\mathbf{c}\) is equal to

121277 A plane \(x\) passes through the point \((1,1,1)\). If \(b, c\), a are the direction ratios of a normal to the plane, where \(\mathbf{a}, \mathbf{b}, \mathbf{c}(\mathbf{a}\lt \mathbf{b}\lt \mathbf{c})\) are the factors of 2001,then the equation of the plane is

121279 If the plane \(56 x+4 y+9 z=2016\) meets the coordinated axes in \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) then the centroid of the triangle \(\mathrm{ABC}\) is

121280 The plane \(3 x+4 y+6 z+7=0\) is rotated about the line \(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}-\mathbf{3} \hat{\mathbf{k}})+(\mathbf{2} \hat{\mathbf{i}}-\mathbf{3} \hat{\mathbf{j}}+\hat{\mathbf{k}})\) unit the plane passes through origin. The equation of the plane in the new position is

121275 In three dimensional space \(x^2-5 x+6=0\) represents

121276 If the equation of the plane passing through the line of intersection of the planes \(2 x-y+z=3\), \(4 x-3 y+5 z+9=0\) and parallel to the line \(\frac{x+1}{-2}=\frac{y+3}{4}=\frac{z-2}{5}\) is \(a x+b y+c z+6=0\). Then \(\mathbf{a}+\mathbf{b}+\mathbf{c}\) is equal to

121277 A plane \(x\) passes through the point \((1,1,1)\). If \(b, c\), a are the direction ratios of a normal to the plane, where \(\mathbf{a}, \mathbf{b}, \mathbf{c}(\mathbf{a}\lt \mathbf{b}\lt \mathbf{c})\) are the factors of 2001,then the equation of the plane is

121279 If the plane \(56 x+4 y+9 z=2016\) meets the coordinated axes in \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) then the centroid of the triangle \(\mathrm{ABC}\) is

121280 The plane \(3 x+4 y+6 z+7=0\) is rotated about the line \(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}-\mathbf{3} \hat{\mathbf{k}})+(\mathbf{2} \hat{\mathbf{i}}-\mathbf{3} \hat{\mathbf{j}}+\hat{\mathbf{k}})\) unit the plane passes through origin. The equation of the plane in the new position is

121275 In three dimensional space \(x^2-5 x+6=0\) represents

121276 If the equation of the plane passing through the line of intersection of the planes \(2 x-y+z=3\), \(4 x-3 y+5 z+9=0\) and parallel to the line \(\frac{x+1}{-2}=\frac{y+3}{4}=\frac{z-2}{5}\) is \(a x+b y+c z+6=0\). Then \(\mathbf{a}+\mathbf{b}+\mathbf{c}\) is equal to

121277 A plane \(x\) passes through the point \((1,1,1)\). If \(b, c\), a are the direction ratios of a normal to the plane, where \(\mathbf{a}, \mathbf{b}, \mathbf{c}(\mathbf{a}\lt \mathbf{b}\lt \mathbf{c})\) are the factors of 2001,then the equation of the plane is

121279 If the plane \(56 x+4 y+9 z=2016\) meets the coordinated axes in \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) then the centroid of the triangle \(\mathrm{ABC}\) is

121280 The plane \(3 x+4 y+6 z+7=0\) is rotated about the line \(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}-\mathbf{3} \hat{\mathbf{k}})+(\mathbf{2} \hat{\mathbf{i}}-\mathbf{3} \hat{\mathbf{j}}+\hat{\mathbf{k}})\) unit the plane passes through origin. The equation of the plane in the new position is

121275 In three dimensional space \(x^2-5 x+6=0\) represents

121276 If the equation of the plane passing through the line of intersection of the planes \(2 x-y+z=3\), \(4 x-3 y+5 z+9=0\) and parallel to the line \(\frac{x+1}{-2}=\frac{y+3}{4}=\frac{z-2}{5}\) is \(a x+b y+c z+6=0\). Then \(\mathbf{a}+\mathbf{b}+\mathbf{c}\) is equal to

121277 A plane \(x\) passes through the point \((1,1,1)\). If \(b, c\), a are the direction ratios of a normal to the plane, where \(\mathbf{a}, \mathbf{b}, \mathbf{c}(\mathbf{a}\lt \mathbf{b}\lt \mathbf{c})\) are the factors of 2001,then the equation of the plane is

121279 If the plane \(56 x+4 y+9 z=2016\) meets the coordinated axes in \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) then the centroid of the triangle \(\mathrm{ABC}\) is

121280 The plane \(3 x+4 y+6 z+7=0\) is rotated about the line \(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}-\mathbf{3} \hat{\mathbf{k}})+(\mathbf{2} \hat{\mathbf{i}}-\mathbf{3} \hat{\mathbf{j}}+\hat{\mathbf{k}})\) unit the plane passes through origin. The equation of the plane in the new position is