NDA 2016 Paper 2 | Three Dimensional Geometry Question 7 | Mathematics

Consider the following statements.

I. The direction ratios of the segment PQ are <3, $$-$$2, 2>

II. The sum of the squares of direction cosines of the line segment PQ is unity.

Which of the above statements is/are correct?

I only

II only

Both I and II

Neither I nor II

NDA 2016 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

A line L passes through the point P(5, $$-$$6, 7) and is parallel to the planes x + y + z = 1 and 2x $$-$$ y $$-$$ 2z = 3.

What are the direction ratios of the line of intersection of the given planes?

< 1, 4, 3 >

< $$-$$ 1, $$-$$ 4, 3 >

< 1, $$-$$4, 3 >

< 1, $$-$$4, $$-$$3 >

NDA 2016 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

A line L passes through the point P(5, $$-$$6, 7) and is parallel to the planes x + y + z = 1 and 2x $$-$$ y $$-$$ 2z = 3.

What is the equation of the line L ?

$${{x - 5} \over { - 1}} = {{y + 6} \over 4} = {{z - 7} \over { - 3}}$$

$${{x + 5} \over { - 1}} = {{y - 6} \over 4} = {{z + 7} \over { - 3}}$$

$${{x - 5} \over { - 1}} = {{y + 6} \over { - 4}} = {{z - 7} \over 3}$$

$${{x - 5} \over { - 1}} = {{y + 6} \over { - 4}} = {{z - 7} \over { - 3}}$$

NDA 2016 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

A plane P passes through the line of intersection of the planes 2x $$-$$ y + 3z = 2, x + y $$-$$ z = 1 and the point (1, 0, 1).

What are the direction ratios of the line of intersection of the given planes?

< 2, $$-$$5, $$-$$3 >

< 1, $$-$$5, $$-$$3 >

< 2, 5, 3 >

< 1, 3, 5 >

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