NDA 2018 Paper 2 | Three Dimensional Geometry Question 27 | Mathematics

Consider the following statements

1. The angle between the planes 2x $$-$$ y + z = 1 and x + y + 2z = 3 is $${\pi \over 3}$$

2. The distance between the planes 6x $$-$$ 3y + 6z + 2 = 0 and 2x $$-$$ y + 2z + 4 = 0 is $${{10} \over 9}$$

Which of the above statement is/are correct?

Only 1

Only 2

Both 1 and 2

Neither 1 nor 2

NDA 2018 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

Let the coordinates of the points A, B, C be (1, 8, 4), (0, $$-$$11, 4) and (2, $$-$$3, 1) respectively. What are the coordinates of the point D which is the foot of the perpendicular from A on BC ?

(3, 4, $$-$$2)

(4, $$-$$2, 5)

(4, 5, $$-$$2)

(2, 4, 5)

NDA 2018 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

What is the equation of the plane passing through the points ($$-$$2, 6, $$-$$6), ($$-$$3, 10, $$-$$9) and ($$-$$5, 0, $$-$$6) ?

2x $$-$$ y $$-$$ 2z = 2

2x + y + 3z = 3

x + y + z = 6

x $$-$$ y $$-$$ z = 3

NDA 2018 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

A sphere of constant radius r through the origin intersects the coordinate axes in A, B and C. What is the locus of the centroid of the $$\Delta$$ABC ?

$${x^2} + {y^2} + {z^2} = {r^2}$$

$${x^2} + {y^2} + {z^2} = 4{r^2}$$

$$9({x^2} + {y^2} + {z^2}) = 4{r^2}$$

$$3({x^2} + {y^2} + {z^2}) = 2{r^2}$$

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