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.
Three Dimensional Geometry Class 12 MCQs Questions with Answers
Three Dimensional Geometry Class 12 MCQ Questions Chapter 11 Question 1.
The direction cosines of the y-axis are
(a) (6, 0, 0)
(b) (1, 0, 0)
(c) (0, 1, 0)
(d) (0, 0, 1)
Answer
Answer: (c) (0, 1, 0)
MCQ On Three Dimensional Geometry Class 12 Chapter 11 Question 2.
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
Answer
Answer: (d) x2 – x1, y2 – y1, z2 – z1
3d Geometry Deals With MCQ Class 12 Chapter 11 Question 3.
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)
Answer
Answer: (d) (5, 0, 6)
MCQ On 3d Geometry Class 12 Chapter 11 Question 4.
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
Answer
Answer: (c) a1a2 + b1b2 + c1c2 = 0
3d Geometry Class 12 MCQ Chapter 11 Question 5.
The distance of the plane 2x – 3y + 6z + 7 = 0 from the point (2, -3, -1) is
(a) 4
(b) 3
(c) 2
(d) \(\frac{1}{5}\)
Answer
Answer: (c) 2
MCQ Questions For Class 12 Maths With Answers Chapter 11 Question 6.
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
Answer
Answer: (a) \(\frac{2}{7}\), \(\frac{-3}{7}\), \(\frac{-6}{7}\)
MCQ Questions For Class 12 Maths With Answers Pdf Download Question 7.
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
Answer
Answer: (c) 2x + 5y – 6z + k = 0
Class 12 Maths MCQ Pdf Chapter 11 Question 8.
(2, – 3, – 1) 2x – 3y + 6z + 7 = 0
(a) 4
(b) 3
(c) 2
(d) \(\frac{1}{5}\)
Answer
Answer: (c) 2
Class 12 Maths Chapter 11 Important Questions Question 9.
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
Answer
Answer: (d) 2
3d Geometry Class 12 Important Questions Chapter 11 Question 10.
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) \(\frac{|\vec{b}.\vec{c}|}{|\vec {a}|}\)
Answer
Answer: (a) 0
Class 12 Maths MCQ Pdf Free Download Chapter 11 Question 11.
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
Answer
Answer: (b) two plane are right angles
Maths MCQ Questions Class 12 Chapter 11 Question 12.
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
Answer
Answer: (d) 1, 1, 0
Class 12 Maths MCQs Chapter Wise Chapter 11 Question 13.
How many lines through the origin in make equal angles with the coordinate axis?
(a) 1
(b) 4
(c) 8
(d) 2
Answer
Answer: (c) 8
Class 12 Maths MCQ Pdf Download Chapter 11 Question 14.
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
Answer
Answer: (c) \(\frac{1}{√2}\), – \(\frac{1}{√2}\)
MCQ Questions For Class 12 Maths With Solutions Chapter 11 Question 15.
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
Answer
Answer: (a) A pair of parallel planes
Maths MCQs For Class 12 With Answers Pdf Chapter 11 Question 16.
The distance of the point (-3, 4, 5) from the origin
(a) 50
(b) 5√2
(c) 6
(d) None of these
Answer
Answer: (b) 5√2
Three Dimensional Element Is MCQ Class 12 Chapter 11 Question 17.
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) \(\frac{3}{2}\)
Answer
Answer: (b) 1
Ncert Solutions For Class 12 Maths Chapter 11 Question 18.
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
Answer
Answer: (a) \(\frac{1}{\sqrt{35}}\), \(\frac{3}{\sqrt{35}}\), \(\frac{5}{\sqrt{35}}\)
Class 12 Maths MCQs Chapter 11 Question 19.
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
Answer
Answer: (a) 7, 4,-2
MCQ Questions For Class 12th Maths Chapter 11 Question 20.
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
Answer
Answer: (b) -3, 7, 5
Question 21.
The lines of intersection of the planes \(\vec{r}\)(3\(\hat{i}\) – \(\hat{j}\) + \(\hat{k}\)) = 1 and \(\vec{r}\)(\(\hat{i}\) +4\(\hat{j}\) – 2\(\hat{k}\)) = 2 is parallel to the vector
(a) 2\(\hat{i}\) + 7\(\hat{j}\) + 13\(\hat{k}\)
(b) -2\(\hat{i}\) + 7\(\hat{j}\) + 13\(\hat{k}\)
(c) 2\(\hat{i}\) – 7\(\hat{j}\) + 13\(\hat{i}\)
(b) -2\(\hat{i}\) – 7\(\hat{j}\) – 13\(\hat{k}\)
Answer
Answer: (b) -2\(\hat{i}\) + 7\(\hat{j}\) + 13\(\hat{k}\)
Question 22.
The equation of the plane through the origin and parallel to the plane 3x – 4y + 5z + 6 = 0
(a) 3x – 4y – 5z – 6 = 0
(b) 3x – 4y + 5z + 6 = 0
(c) 3x – 4y + 5z = 0
(d) 3x + 4y – 5z + 6 = 0
Answer
Answer: (c) 3x – 4y + 5z = 0
Question 23.
The locus of xy + yz = 0 is
(a) A pair of st. lines
(b) A pair of parallel lines
(c) A pair of parallel planes
(d) A pair of perpendicular planes
Answer
Answer: (d) A pair of perpendicular planes
Question 24.
The plane x + y = 0
(a) is parallel to z-axis
(b) is perpendicular to z-axis
(c) passes through z-axis
(d) None of these
Answer
Answer: (c) passes through z-axis
Question 25.
If α, β, γ are the angle which a half ray makes with the positive directions of the axis then sin²α + sin²β + sin²γ =
(a) 1
(b) 2
(c) 0
(d) -1
Answer
Answer: (b) 2
Question 26.
If a line makes angles α, β, γ with the axis then cos 2α + cos 2β + cos 2γ =
(a) -2
(b) -1
(c) 1
(d) 2
Answer
Answer: (b) -1
Question 27.
The line x = 1, y = 2 is
(a) parallel to x-axis
(b) parallel to y-axis
(c) parallel to z-axis
(d) None of these
Answer
Answer: (c) parallel to z-axis
Question 28.
The points A (1, 1, 0), B(0, 1, 1), C(1, 0, 1) and D(\(\frac{2}{3}\), \(\frac{2}{3}\), \(\frac{2}{3}\))
(a) Coplanar
(b) Non-coplanar
(c) Vertices of a parallelogram
(d) None of these
Answer
Answer: (a) Coplanar
Question 29.
The angle between the planes 2x – y + z = 6 and x + y + 2z = 7 is
(a) \(\frac{π}{4}\)
(b) \(\frac{π}{6}\)
(c) \(\frac{π}{3}\)
(d) \(\frac{π}{2}\)
Answer
Answer: (c) \(\frac{π}{3}\)
Question 30.
The distance of the points (2, 1, -1) from the plane x- 2y + 4z – 9 is
(a) \(\frac{\sqrt{31}}{21}\)
(b) \(\frac{13}{21}\)
(c) \(\frac{13}{\sqrt{21}}\)
(d) \(\sqrt{\frac{π}{2}}\)
Answer
Answer: (c) \(\frac{13}{\sqrt{21}}\)
Question 31.
The planes \(\vec{r}\)(2\(\hat{i}\) + 3\(\hat{j}\) – 6\(\hat{k}\)) = 7 and
\(\vec{r}\)(\(\frac{-2}{7}\)\(\vec{i}\) – \(\frac{3}{j}\)\(\vec{j}\) + \(\frac{6}{7}\)\(\vec{k}\)) = 0 are
(a) parallel
(b) at right angles
(c) equidistant front origin
(d) None of these
Answer
Answer: (a) parallel
Question 32.
The equation of the plane through point (1, 2, -3) which is parallel to the plane 3x- 5y + 2z = 11 is given by
(a) 3x – 5y + 2z – 13 = 0
(b) 5x – 3y + 2z + 13 = 0
(c) 3x – 2y + 5z + 13 = 0
(d) 3x – 5y + 2z + 13 = 0
Answer
Answer: (d) 3x – 5y + 2z + 13 = 0
Question 33.
Distance of the point (a, β, γ) from y-axis is
(a) β
(b) |β|
(c) |β + γ|
(d) \(\sqrt{α^2+γ^2}\)
Answer
Answer: (d) \(\sqrt{α^2+γ^2}\)
Question 34.
If the directions cosines of a line are A, k, k, then
(a) k > 0
(b) 0 < k < 1
(c) k = 1
(d) k = \(\frac{1}{√3}\) or –\(\frac{1}{√3}\)
Answer
Answer: (d) k = \(\frac{1}{√3}\) or –\(\frac{1}{√3}\)
Question 35.
The distance of the plane \(\vec{r}\)(\(\frac{-2}{7}\)\(\hat{i}\) – \(\frac{3}{7}\)\(\hat{j}\) + \(\frac{6}{7}\)\(\hat{k}\)) = 0 from the orgin is
(a) 1
(b) 7
(c) \(\frac{1}{7}\)
(d) None of these
Answer
Answer: (a) 1
Question 36.
The sine of the angle between the straight line \(\frac{x-2}{3}\) = \(\frac{y-3}{4}\) = \(\frac{z-4}{5}\) and the plane 2x – 2y + z = 5 is
(a) \(\frac{10}{6√5}\)
(b) \(\frac{4}{5√2}\)
(c) \(\frac{2√3}{5}\)
(d) \(\sqrt{\frac{√2}{10}}\)
Answer
Answer: (c) \(\frac{2√3}{5}\)
Question 37.
The reflection of the point (a, β, γ) in the xy-plane is
(a) (α, β, 0)
(b) (0, 0, γ)
(c) (- α, – β, γ)
(d) (α, β, γ)
Answer
Answer: (d) (α, β, γ)
Question 38.
The area of the quadrilateral ABCD, where A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2) is equal to
(a) 9 sq. units
(b) 18 sq. units
(c) 27 sq. units
(d) 81 sq. units
Answer
Answer: (a) 9 sq. units
Question 39.
The plane 2x – 3y + 6z – 11 = 0 makes an angle sin-1 (α) with .e-axis. The value of a is equal to
(a) \(\frac{√3}{2}\)
(b) \(\frac{√2}{3}\)
(c) \(\frac{2}{7}\)
(d) \(\frac{3}{7}\)
Answer
Answer: (c) \(\frac{2}{7}\)
Question 40.
The cosines of the angle between any two diagonals of a cube is
(a) \(\frac{1}{3}\)
(b) \(\frac{1}{2}\)
(c) \(\frac{2}{3}\)
(d) \(\frac{1}{√3}\)
Answer
Answer: (a) \(\frac{1}{3}\)
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