NDA 2017 Paper 2 | Three Dimensional Geometry Question 17 | Mathematics

A variable plane passes through a fixed point (a, b, c) and cuts the axes in A, B, and C respectively. The locus of the centre of the sphere OABC, O being the origin, is

$${x \over a} + {y \over b} + {z \over c} = 1$$

$${a \over x} + {b \over y} + {c \over z} = 1$$

$${a \over x} + {b \over y} + {c \over z} = 2$$

$${x \over a} + {y \over b} + {z \over c} = 2$$

NDA 2017 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

The equation of the plane passing through the line of intersection of the planes x + y + z = 1, 2x + 3y + 4z = 7, and perpendicular to the plane x $$-$$ 5y + 3z = 5 is given by

x + 2y + 3z $$-$$ 6 = 0

x + 2y + 3z + 6 = 0

3x + 4y + 5z $$-$$ 8 = 0

3x + 4y + 5z + 8 = 0

NDA 2017 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

A straight line with direction cosines <0, 1, 0> is

parallel to X-axis

parallel to Y-axis

parallel to Z-axis

equally inclined to all the axes

NDA 2017 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

(0, 0, 0), (a, 0, 0), (0, b, 0) and (0, 0, c) are four distinct points. What are the coordinates of the point which is equidistant from the four points?

$$\left( {{{a + b + c} \over 3},{{a + b + c} \over 3},{{a + b + c} \over 3}} \right)$$

(a, b, c)

$$\left( {{a \over 2},{b \over 2},{c \over 2}} \right)$$

$$\left( {{a \over 3},{b \over 3},{c \over 3}} \right)$$

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