NDA 2019 Paper 2 | Three Dimensional Geometry Question 35 | Mathematics

A straight line passes through the point (1, 1, 1) makes an angle 60$$^\circ$$ with the positive direction of Z-axis, and the cosine of the angles made by it with the positive directions of the Y-axis and the X-axis are in the ratio $$\sqrt 3 $$ : 1. What is the acute angle between the two possible positions of the line?

90$$^\circ$$

60$$^\circ$$

45$$^\circ$$

30$$^\circ$$

NDA 2019 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

A point on a line has coordinates (p + 1, p $$-$$ 3, $$\sqrt 2 $$p) where p is any real number. What are the direction cosines of the line?

$${1 \over 2},{1 \over 2},{1 \over {\sqrt 2 }}$$

$${1 \over {\sqrt 2 }},{1 \over 2},{1 \over 2}$$

$${1 \over {\sqrt 2 }},{1 \over 2}, - {1 \over 2}$$

Cannot be determined due to insufficient data

NDA 2019 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

The centroid of the triangle with vertices A(2, $$-$$3, 3), B(5, $$-$$3, $$-$$4) and C(2, $$-$$3, $$-$$2) is the point

($$-$$3, 3, $$-$$1)

(3, $$-$$3, $$-$$1)

(3, 1, $$-$$3)

($$-$$3, $$-$$1, $$-$$3)

NDA 2019 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

What is the radius of the sphere $${x^2} + {y^2} + {z^2} - 6x + 8y - 10z + 1 = 0$$ ?

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