NDA 2018 Paper 1 | Three Dimensional Geometry Question 28 | Mathematics

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 ?

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

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

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

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

NDA 2018 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

The coordinates of the vertices P, Q and R of a triangle PQR are (1, $$-$$1, 1), (3, $$-$$2, 2) and (0, 2, 6) respectively. If $$\angle$$RQP = $$\theta$$, then what is $$\angle$$PRQ equal to?

30$$^\circ$$ + $$\theta$$

45$$^\circ$$ $$-$$ $$\theta$$

60$$^\circ$$ $$-$$ $$\theta$$

90$$^\circ$$ $$-$$ $$\theta$$

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