Equation of a Line, Sphere, and a Plane in Different Forms
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Three Dimensional Geometry

121291 The value of \(\lambda\) for which the straight line \(\frac{x-\lambda}{3}=\frac{y-1}{2+\lambda}=\frac{z-3}{-1}\) may lie on the place \(x-2 y\) \(=\mathbf{0}\), is

1 2
2 0
3 \(-\frac{1}{2}\)
4 There is no such \(\lambda\)
WB JEE-2015
Three Dimensional Geometry

121292 The least positive value of \(t\), so that the lines \(x=\) \(t+\alpha, y+16=0\) and \(y=\alpha x\) are concurrent, is

1 2
2 4
3 16
4 8
WB JEE-2015
Three Dimensional Geometry

121293 A plane cute the coordinate axes \(X, Y, Z\) at \(A\), \(B, C\) respectively such that the centroid of the \(\triangle A B C\) is \((6,6,3)\). Then the equation of that plane is

1 \(x+y+z-6=0\)
2 \(x+2 y+z-18=0\)
3 \(2 x+y+z-18=0\)
4 \(x+y+2 z-18=0\)
AP EAMCET-22.04.2018
Three Dimensional Geometry

121294 The equation of the plane whose intercepts on \(x, y, z\) axes are \(1,2,4\) respectively is

1 \(4 x+2 y+z=4\)
2 \(4 x+2 y+z=2\)
3 \(4 x+2 y+z=1\)
4 \(x+2 y+4 z=0\)
AP EAMCET-21.09.2020
Three Dimensional Geometry

121295 The equation of the plane through the intersection of the planes \(x+y+z=1\) and \(2 x+\) \(3 y-z+4=0\) and parallel to the \(x\)-axis is

1 \(y+3 z+6=0\)
2 \(y+3 z-6=0\)
3 \(y-3 z+6=0\)
4 \(y-3 z-6=0\)
WB JEE-2022
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Three Dimensional Geometry

121291 The value of \(\lambda\) for which the straight line \(\frac{x-\lambda}{3}=\frac{y-1}{2+\lambda}=\frac{z-3}{-1}\) may lie on the place \(x-2 y\) \(=\mathbf{0}\), is

1 2
2 0
3 \(-\frac{1}{2}\)
4 There is no such \(\lambda\)
WB JEE-2015
Three Dimensional Geometry

121292 The least positive value of \(t\), so that the lines \(x=\) \(t+\alpha, y+16=0\) and \(y=\alpha x\) are concurrent, is

1 2
2 4
3 16
4 8
WB JEE-2015
Three Dimensional Geometry

121293 A plane cute the coordinate axes \(X, Y, Z\) at \(A\), \(B, C\) respectively such that the centroid of the \(\triangle A B C\) is \((6,6,3)\). Then the equation of that plane is

1 \(x+y+z-6=0\)
2 \(x+2 y+z-18=0\)
3 \(2 x+y+z-18=0\)
4 \(x+y+2 z-18=0\)
AP EAMCET-22.04.2018
Three Dimensional Geometry

121294 The equation of the plane whose intercepts on \(x, y, z\) axes are \(1,2,4\) respectively is

1 \(4 x+2 y+z=4\)
2 \(4 x+2 y+z=2\)
3 \(4 x+2 y+z=1\)
4 \(x+2 y+4 z=0\)
AP EAMCET-21.09.2020
Three Dimensional Geometry

121295 The equation of the plane through the intersection of the planes \(x+y+z=1\) and \(2 x+\) \(3 y-z+4=0\) and parallel to the \(x\)-axis is

1 \(y+3 z+6=0\)
2 \(y+3 z-6=0\)
3 \(y-3 z+6=0\)
4 \(y-3 z-6=0\)
WB JEE-2022
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Three Dimensional Geometry

121291 The value of \(\lambda\) for which the straight line \(\frac{x-\lambda}{3}=\frac{y-1}{2+\lambda}=\frac{z-3}{-1}\) may lie on the place \(x-2 y\) \(=\mathbf{0}\), is

1 2
2 0
3 \(-\frac{1}{2}\)
4 There is no such \(\lambda\)
WB JEE-2015
Three Dimensional Geometry

121292 The least positive value of \(t\), so that the lines \(x=\) \(t+\alpha, y+16=0\) and \(y=\alpha x\) are concurrent, is

1 2
2 4
3 16
4 8
WB JEE-2015
Three Dimensional Geometry

121293 A plane cute the coordinate axes \(X, Y, Z\) at \(A\), \(B, C\) respectively such that the centroid of the \(\triangle A B C\) is \((6,6,3)\). Then the equation of that plane is

1 \(x+y+z-6=0\)
2 \(x+2 y+z-18=0\)
3 \(2 x+y+z-18=0\)
4 \(x+y+2 z-18=0\)
AP EAMCET-22.04.2018
Three Dimensional Geometry

121294 The equation of the plane whose intercepts on \(x, y, z\) axes are \(1,2,4\) respectively is

1 \(4 x+2 y+z=4\)
2 \(4 x+2 y+z=2\)
3 \(4 x+2 y+z=1\)
4 \(x+2 y+4 z=0\)
AP EAMCET-21.09.2020
Three Dimensional Geometry

121295 The equation of the plane through the intersection of the planes \(x+y+z=1\) and \(2 x+\) \(3 y-z+4=0\) and parallel to the \(x\)-axis is

1 \(y+3 z+6=0\)
2 \(y+3 z-6=0\)
3 \(y-3 z+6=0\)
4 \(y-3 z-6=0\)
WB JEE-2022
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Three Dimensional Geometry

121291 The value of \(\lambda\) for which the straight line \(\frac{x-\lambda}{3}=\frac{y-1}{2+\lambda}=\frac{z-3}{-1}\) may lie on the place \(x-2 y\) \(=\mathbf{0}\), is

1 2
2 0
3 \(-\frac{1}{2}\)
4 There is no such \(\lambda\)
WB JEE-2015
Three Dimensional Geometry

121292 The least positive value of \(t\), so that the lines \(x=\) \(t+\alpha, y+16=0\) and \(y=\alpha x\) are concurrent, is

1 2
2 4
3 16
4 8
WB JEE-2015
Three Dimensional Geometry

121293 A plane cute the coordinate axes \(X, Y, Z\) at \(A\), \(B, C\) respectively such that the centroid of the \(\triangle A B C\) is \((6,6,3)\). Then the equation of that plane is

1 \(x+y+z-6=0\)
2 \(x+2 y+z-18=0\)
3 \(2 x+y+z-18=0\)
4 \(x+y+2 z-18=0\)
AP EAMCET-22.04.2018
Three Dimensional Geometry

121294 The equation of the plane whose intercepts on \(x, y, z\) axes are \(1,2,4\) respectively is

1 \(4 x+2 y+z=4\)
2 \(4 x+2 y+z=2\)
3 \(4 x+2 y+z=1\)
4 \(x+2 y+4 z=0\)
AP EAMCET-21.09.2020
Three Dimensional Geometry

121295 The equation of the plane through the intersection of the planes \(x+y+z=1\) and \(2 x+\) \(3 y-z+4=0\) and parallel to the \(x\)-axis is

1 \(y+3 z+6=0\)
2 \(y+3 z-6=0\)
3 \(y-3 z+6=0\)
4 \(y-3 z-6=0\)
WB JEE-2022
Join With Us for More Updates
Three Dimensional Geometry

121291 The value of \(\lambda\) for which the straight line \(\frac{x-\lambda}{3}=\frac{y-1}{2+\lambda}=\frac{z-3}{-1}\) may lie on the place \(x-2 y\) \(=\mathbf{0}\), is

1 2
2 0
3 \(-\frac{1}{2}\)
4 There is no such \(\lambda\)
WB JEE-2015
Three Dimensional Geometry

121292 The least positive value of \(t\), so that the lines \(x=\) \(t+\alpha, y+16=0\) and \(y=\alpha x\) are concurrent, is

1 2
2 4
3 16
4 8
WB JEE-2015
Three Dimensional Geometry

121293 A plane cute the coordinate axes \(X, Y, Z\) at \(A\), \(B, C\) respectively such that the centroid of the \(\triangle A B C\) is \((6,6,3)\). Then the equation of that plane is

1 \(x+y+z-6=0\)
2 \(x+2 y+z-18=0\)
3 \(2 x+y+z-18=0\)
4 \(x+y+2 z-18=0\)
AP EAMCET-22.04.2018
Three Dimensional Geometry

121294 The equation of the plane whose intercepts on \(x, y, z\) axes are \(1,2,4\) respectively is

1 \(4 x+2 y+z=4\)
2 \(4 x+2 y+z=2\)
3 \(4 x+2 y+z=1\)
4 \(x+2 y+4 z=0\)
AP EAMCET-21.09.2020
Three Dimensional Geometry

121295 The equation of the plane through the intersection of the planes \(x+y+z=1\) and \(2 x+\) \(3 y-z+4=0\) and parallel to the \(x\)-axis is

1 \(y+3 z+6=0\)
2 \(y+3 z-6=0\)
3 \(y-3 z+6=0\)
4 \(y-3 z-6=0\)
WB JEE-2022