MCQ Questions for Class 12 Maths Chapter 11 Three Dimensional Geometry with Answers Set-A

Three Dimensional Geometry Class 12 Maths MCQs Questions with Answers

Check the below NCERT MCQ Questions for Class 12 Maths Chapter 11 Three Dimensional Geometry with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have Provided Three Dimensional Geometry Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

Class 12 Maths Chapter 11 Quiz

Class 12 Maths Chapter 11 MCQ Online Test

You can refer to NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry to revise the concepts in the syllabus effectively and improve your chances of securing high marks in your board exams.

Three Dimensional Geometry Class 12 Maths MCQ online test

Q1.	The direction cosines of the y-axis are
	A. (6, 0, 0)
	B. (1, 0, 0)
	C. (0, 1, 0)
	D. (0, 0, 1)

Ans: (0, 1, 0)

Q2.	The direction ratios of the line joining the points (x, y, z) and (x₂, y₂, z₁) are
	A. x₁ + x₂, y₁ + y₂, z₁ + z₂
	B. \(\sqrt{(x_1 – x_2)^2 + (y_1 – y_2)^2 + (z_1 + z_2)^2}\)
	C. \(\frac{x_1+x_2}{2}\), \(\frac{y_1+y_2}{2}\), \(\frac{z_1+z_2}{2}\)
	D. x₂ – x₁, y₂ – y₁, z₂ – z₁

Ans: x₂ – x₁, y₂ – y₁, z₂ – z₁

Q3.	The coordinates of the midpoints of the line segment joining the points (2, 3, 4) and (8, -3, 8) are
	A. (10, 0, 12)
	B. (5, 6, 0)
	C. (6, 5, 0)
	D. (5, 0, 6)

Ans: (5, 0, 6)

Q4.	If the planes a₁x + b, y + c, z + d₁ = 0 and a₂x + b, y + c₂z + d₂ = 0 are perpendicular to each other then
	A. \(\frac{a_1}{a_2}\) = \(\frac{b_1}{b_2}\) = \(\frac{c_1}{c_2}\)
	B. \(\frac{a_1}{a_2}\) + \(\frac{b_1}{b_2}\), \(\frac{c_1}{c_2}\)
	C. a₁a₂ + b₁b₂ + c₁c₂ = 0
	D. a\(_{1}^{2}\)a\(_{2}^{2}\) + b\(_{1}^{2}\)b\(_{2}^{2}\) + c\(_{1}^{2}\)c\(_{2}^{2}\) = 0

Ans: a₁a₂ + b₁b₂ + c₁c₂ = 0

Q5.	The distance of the plane 2x – 3y + 6z + 7 = 0 from the point (2, -3, -1) is
	A. 4
	B. 3
	C. 2
	D. \(\frac{1}{5}\)

Ans: 2

Q6.	The direction cosines of the normal to the plane 2x – 3y – 6z – 3 = 0 are
	A. \(\frac{2}{7}\), \(\frac{-3}{7}\), \(\frac{-6}{7}\)
	B. \(\frac{2}{7}\), \(\frac{3}{7}\), \(\frac{6}{7}\)
	C. \(\frac{-2}{7}\), \(\frac{-3}{7}\), \(\frac{-6}{7}\)
	D. None of these

Ans: \(\frac{2}{7}\), \(\frac{-3}{7}\), \(\frac{-6}{7}\)

Q7.	If 2x + 5y – 6z + 3 = 0 be the equation of the plane, then the equation of any plane parallel to the given plane is
	A. 3x + 5y – 6z + 3 = 0
	B. 2x – 5y – 6z + 3 = 0
	C. 2x + 5y – 6z + k = 0
	D. None of these

Ans: 2x + 5y – 6z + k = 0

Q8.	(2, – 3, – 1) 2x – 3y + 6z + 7 = 0
	A. 4
	B. 3
	C. 2
	D. \(\frac{1}{5}\)

Ans: 2

Q9.	The length of the ⊥^er from the point (0, – 1, 3) to the plane 2x + y – 2z + 1 = 0 is
	A. 0
	B. 2√3
	C. \(\frac{2}{3}\)
	D. 2

Ans: 2

Q10.	The shortest distance between the lines \(\vec{r}\) = \(\vec{a}\) + k\(\vec{b}\) and r = \(\vec{a}\) + l\(\vec{c}\) is (\(\vec{b}\) and \(\vec{c}\) are non-collinear)
	A. 0
	B. \|\(\vec{b}\).\(\vec{c}\)\|
	C. \(\frac{\|\vec{b}×\vec{c}\|}{\|\vec {a}\|}\)
	D. \(\frac{\|\vec{b}.\vec{c}\|}{\|\vec {a}\|}\)

Ans: 0

Q11.	The equation xy = 0 in three dimensional space is represented by
	A. a plane
	B. two plane are right angles
	C. a pair of parallel planes
	D. a pair of st. line

Ans: two plane are right angles

Q12.	The direction cosines of any normal to the xy plane are
	A. 1, 0 ,0
	B. 0, 1, 0
	C. 1, 1, 0
	D. 1, 1, 0

Ans: 1, 1, 0

Q13.	How many lines through the origin in make equal angles with the coordinate axis?
	A. 1
	B. 4
	C. 8
	D. 2

Ans: 8

Q14.	The direction cosines of the line joining (1, -1, 1) and (-1, 1, 1) are
	A. 2, -2, 0
	B. 1, -1, 0
	C. \(\frac{1}{√2}\), – \(\frac{1}{√2}\)
	D. None of these

Ans: \(\frac{1}{√2}\), – \(\frac{1}{√2}\)

Q15.	The equation x² – x – 2 = 0 in three dimensional space is represented by
	A. A pair of parallel planes
	B. A pair of straight lines
	C. A pair of perpendicular plane
	D. None of these

Ans: A pair of parallel planes

Q16.	The distance of the point (-3, 4, 5) from the origin
	A. 50
	B. 5√2
	C. 6
	D. None of these

Ans: 5√2

Q17.	If a line makes angles Q₁, Q₂₁ and Q₃ respectively with the coordinate axis then the value of cos² Q₁ + cos² Q₂ + cos² Q₃
	A. 2
	B. 1
	C. 4
	D. \(\frac{3}{2}\)

Ans: 1

Q18.	The direction ratios of a line are 1,3,5 then its direction cosines are
	A. \(\frac{1}{\sqrt{35}}\), \(\frac{3}{\sqrt{35}}\), \(\frac{5}{\sqrt{35}}\)
	B. \(\frac{1}{9}\), \(\frac{1}{3}\), \(\frac{5}{9}\)
	C. \(\frac{5}{\sqrt{35}}\), \(\frac{3}{\sqrt{35}}\), \(\frac{1}{\sqrt{35}}\)
	D. None of these

Ans: \(\frac{1}{\sqrt{35}}\), \(\frac{3}{\sqrt{35}}\), \(\frac{5}{\sqrt{35}}\)

Q19.	The direction ratios of the normal to the plane 7x + 4y – 2z + 5 = 0 are
	A. 7, 4,-2
	B.7, 4, 5
	C. 7, 4, 2
	D. 4, -2, 5

Ans: 7, 4,-2

Q20.	The direction ratios of the line of intersection of the planes 3x + 2y – z = 5 and x – y + 2z = 3 are
	A. 3, 2, -1
	B. -3, 7, 5
	C. 1, -1, 2
	D. – 11, 4, -5

Ans: -3, 7, 5

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