Miscellaneous 3-D Problems
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NEET DIGITAL LIBRARY
Three Dimensional Geometry

121431 A variable plane passes through a fixed point \((\alpha, \beta, \gamma)\) and meets the coordinate axes in \(A, B\) and \(C\). Let \(P_1, P_2\) and \(P_3\) be the planes passing through \(A, B, C\) and parallel to the coordinate planes YZ, ZX, XY respectively. Then, the locus of the point of intersection of the planes \(P_1, P_2\) and \(P_3\) is

1 \(\alpha \mathrm{x}+\beta \mathrm{y}+\gamma \mathrm{z}=1\)
2 \(\frac{\alpha}{\mathrm{x}}+\frac{\beta}{\mathrm{y}}+\frac{\gamma}{\mathrm{z}}=1\)
3 \(\alpha x^2+\beta y^2+\gamma z^2=1\)
4 \(\alpha \beta x+\beta \gamma y+\alpha \gamma z=1\)
AP EAMCET-22.04.2018
Three Dimensional Geometry

121433 The perimeter of the triangle with vertices at \((1,0,0),(0,1,0)\) and \((0,0,1)\) is

1 3
2 2
3 \(2 \sqrt{2}\)
4 \(3 \sqrt{2}\)
AP EAMCET-2009
Three Dimensional Geometry

121434 A variable plane passes through a fixed point \((1,2,3)\) Then, the foot of the perpendicular from the origin to the plane lies on

1 a circle
2 a sphere
3 an ellipse
4 a parabola
AP EAMCET-2013
Three Dimensional Geometry

121435 If the plane \(3 x-2 y-z-18=0\) meets the coordinate axes in \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) then the centroid of \(\triangle \mathrm{ABC}\) is

1 \((2,3,-6)\)
2 \((2,-3,6)\)
3 \((-2,-3,6)\)
4 \((2,-3,-6)\)
AP EAMCET-2004
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Three Dimensional Geometry

121431 A variable plane passes through a fixed point \((\alpha, \beta, \gamma)\) and meets the coordinate axes in \(A, B\) and \(C\). Let \(P_1, P_2\) and \(P_3\) be the planes passing through \(A, B, C\) and parallel to the coordinate planes YZ, ZX, XY respectively. Then, the locus of the point of intersection of the planes \(P_1, P_2\) and \(P_3\) is

1 \(\alpha \mathrm{x}+\beta \mathrm{y}+\gamma \mathrm{z}=1\)
2 \(\frac{\alpha}{\mathrm{x}}+\frac{\beta}{\mathrm{y}}+\frac{\gamma}{\mathrm{z}}=1\)
3 \(\alpha x^2+\beta y^2+\gamma z^2=1\)
4 \(\alpha \beta x+\beta \gamma y+\alpha \gamma z=1\)
AP EAMCET-22.04.2018
Three Dimensional Geometry

121433 The perimeter of the triangle with vertices at \((1,0,0),(0,1,0)\) and \((0,0,1)\) is

1 3
2 2
3 \(2 \sqrt{2}\)
4 \(3 \sqrt{2}\)
AP EAMCET-2009
Three Dimensional Geometry

121434 A variable plane passes through a fixed point \((1,2,3)\) Then, the foot of the perpendicular from the origin to the plane lies on

1 a circle
2 a sphere
3 an ellipse
4 a parabola
AP EAMCET-2013
Three Dimensional Geometry

121435 If the plane \(3 x-2 y-z-18=0\) meets the coordinate axes in \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) then the centroid of \(\triangle \mathrm{ABC}\) is

1 \((2,3,-6)\)
2 \((2,-3,6)\)
3 \((-2,-3,6)\)
4 \((2,-3,-6)\)
AP EAMCET-2004
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NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Three Dimensional Geometry

121431 A variable plane passes through a fixed point \((\alpha, \beta, \gamma)\) and meets the coordinate axes in \(A, B\) and \(C\). Let \(P_1, P_2\) and \(P_3\) be the planes passing through \(A, B, C\) and parallel to the coordinate planes YZ, ZX, XY respectively. Then, the locus of the point of intersection of the planes \(P_1, P_2\) and \(P_3\) is

1 \(\alpha \mathrm{x}+\beta \mathrm{y}+\gamma \mathrm{z}=1\)
2 \(\frac{\alpha}{\mathrm{x}}+\frac{\beta}{\mathrm{y}}+\frac{\gamma}{\mathrm{z}}=1\)
3 \(\alpha x^2+\beta y^2+\gamma z^2=1\)
4 \(\alpha \beta x+\beta \gamma y+\alpha \gamma z=1\)
AP EAMCET-22.04.2018
Three Dimensional Geometry

121433 The perimeter of the triangle with vertices at \((1,0,0),(0,1,0)\) and \((0,0,1)\) is

1 3
2 2
3 \(2 \sqrt{2}\)
4 \(3 \sqrt{2}\)
AP EAMCET-2009
Three Dimensional Geometry

121434 A variable plane passes through a fixed point \((1,2,3)\) Then, the foot of the perpendicular from the origin to the plane lies on

1 a circle
2 a sphere
3 an ellipse
4 a parabola
AP EAMCET-2013
Three Dimensional Geometry

121435 If the plane \(3 x-2 y-z-18=0\) meets the coordinate axes in \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) then the centroid of \(\triangle \mathrm{ABC}\) is

1 \((2,3,-6)\)
2 \((2,-3,6)\)
3 \((-2,-3,6)\)
4 \((2,-3,-6)\)
AP EAMCET-2004
NEET DIGITAL LIBRARY
Three Dimensional Geometry

121431 A variable plane passes through a fixed point \((\alpha, \beta, \gamma)\) and meets the coordinate axes in \(A, B\) and \(C\). Let \(P_1, P_2\) and \(P_3\) be the planes passing through \(A, B, C\) and parallel to the coordinate planes YZ, ZX, XY respectively. Then, the locus of the point of intersection of the planes \(P_1, P_2\) and \(P_3\) is

1 \(\alpha \mathrm{x}+\beta \mathrm{y}+\gamma \mathrm{z}=1\)
2 \(\frac{\alpha}{\mathrm{x}}+\frac{\beta}{\mathrm{y}}+\frac{\gamma}{\mathrm{z}}=1\)
3 \(\alpha x^2+\beta y^2+\gamma z^2=1\)
4 \(\alpha \beta x+\beta \gamma y+\alpha \gamma z=1\)
AP EAMCET-22.04.2018
Three Dimensional Geometry

121433 The perimeter of the triangle with vertices at \((1,0,0),(0,1,0)\) and \((0,0,1)\) is

1 3
2 2
3 \(2 \sqrt{2}\)
4 \(3 \sqrt{2}\)
AP EAMCET-2009
Three Dimensional Geometry

121434 A variable plane passes through a fixed point \((1,2,3)\) Then, the foot of the perpendicular from the origin to the plane lies on

1 a circle
2 a sphere
3 an ellipse
4 a parabola
AP EAMCET-2013
Three Dimensional Geometry

121435 If the plane \(3 x-2 y-z-18=0\) meets the coordinate axes in \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) then the centroid of \(\triangle \mathrm{ABC}\) is

1 \((2,3,-6)\)
2 \((2,-3,6)\)
3 \((-2,-3,6)\)
4 \((2,-3,-6)\)
AP EAMCET-2004
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