Test: Three Dimensional Geometry- Assertion & Reason Type Questions - JEE MCQ

# Test: Three Dimensional Geometry- Assertion & Reason Type Questions - JEE MCQ

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## 6 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Three Dimensional Geometry- Assertion & Reason Type Questions

Test: Three Dimensional Geometry- Assertion & Reason Type Questions for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: Three Dimensional Geometry- Assertion & Reason Type Questions questions and answers have been prepared according to the JEE exam syllabus.The Test: Three Dimensional Geometry- Assertion & Reason Type Questions MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Three Dimensional Geometry- Assertion & Reason Type Questions below.
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Test: Three Dimensional Geometry- Assertion & Reason Type Questions - Question 1

### Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A): The length of the intercepts on the coordinate axes made by the plane 5x + 2y + z – 13 = 0 are 13/5 , 13/2 , 13 unitReason (R): Given: Equation of plane5x + 2y + z - 13 = 0⇒ 5x + 2y + z = 13⇒ ⇒ ∴ Length of intercepts are 13/5 , 13/2 , 13 units

Test: Three Dimensional Geometry- Assertion & Reason Type Questions - Question 2

### Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A): P is a point on the line segment joining the points (3, 2, –1) and (6, –4, –2). If x coordinate of P is 5, then its y coordinate is –2.Reason (R): The two lines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ will be perpendicular, iff aa’ + bb’ + cc’ = 0.

Detailed Solution for Test: Three Dimensional Geometry- Assertion & Reason Type Questions - Question 2
Assertion (A) is correct.

Since P = (5, y, z)

Equation of line joining (3, 2, –1) and (6, –4, –2) is

so if point P lies on the line then it must satisfy the above equation

Hence y co-ordinate of P is –2.

Reason (R) is false.

Since, the two lines x = ay + b, z = cy + d and = a’y + b’, z = c’y + d’ will be perpendicular, iff aa’ + cc’ + 1 = 0.

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Test: Three Dimensional Geometry- Assertion & Reason Type Questions - Question 3

### Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A): If two lines are in the same plane i.e., they are coplanar, they will intersect each other if they are non-parallel. Hence the shortest distance between them is zero.If the lines are parallel then the shortest distance between them will be the perpendicular distance between the lines i.e., the length of the perpendicular drawn from a point on one line onto the other line.Reason (R): The angle between the lines with direction ratio 〈a1 ,b1, c1〉 and 〈a2 ,b2, c2〉 is given by:

Detailed Solution for Test: Three Dimensional Geometry- Assertion & Reason Type Questions - Question 3
Assertion (A) and Reason (R) both are individually correct.
Test: Three Dimensional Geometry- Assertion & Reason Type Questions - Question 4

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A): The angle between the straight lines

Reason (R): Skew lines are lines in different planes which are parallel and intersecting.

Detailed Solution for Test: Three Dimensional Geometry- Assertion & Reason Type Questions - Question 4
Assertion (A) is correct.

Direction ratios of lines are a1 = 2, b1 = 5, c1 = 4 and a2 = 1, b2 = 2, c2 = –3

As we know, The angle between the lines is given by

= 0

∴ θ = 90°

Reason (R) is wrong.

In the space, there are lines neither intersecting nor parallel, such pairs of lines are non-coplanar and are called skew lines.

Test: Three Dimensional Geometry- Assertion & Reason Type Questions - Question 5

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A): Direction cosines of a line are the sines of the angles made by the line with the negative directions of the coordinate axes.

Reason (R): The acute angle between the lines x – 2 = 0 and

Detailed Solution for Test: Three Dimensional Geometry- Assertion & Reason Type Questions - Question 5
Assertion (A) is wrong.

Since, direction cosines of a line are the cosines of the angles made by the line with the positive directions of the coordinate axes.

Reason (R) is correct.

Since, the slope of the line x – 2 = 0 is ∞.

The slope of line

Let m1 = ∞, m2 = √3 and the angle between the given lines is θ.

⇒ θ = 30º

Test: Three Dimensional Geometry- Assertion & Reason Type Questions - Question 6

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A): x2 + y2 + z2 + 4x – 6y – 8z = 7 the equation to the sphere whose centre is at (–2, 3, 4) and radius is 6 units.

Reason (R): Given: Centre is at (–2, 3, 4) and r = 6

⇒ (x0, y0, z0) = (–2, 3, 4) and r = 6

We know that general equation of sphere is (x – x0)2 + (y – y0)2 + (z – z0)2 = r2

⇒ (x – (–2))2 + (y – 3)2 + (z – 4)2 = 62

⇒ (x + 2)2 + (y – 3)2 + (z – 4)2 = 62

⇒ x2 + 4x + 4 + y2 – 6y + 9 + z2 – 8z + 16 = 36

⇒ x2 + y2 + z2 + 4x – 6y – 8z + 29 = 36

⇒ x2 + y2 + z. + 4x – 6y – 8z = 7

## Mathematics (Maths) Class 12

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## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests