{"id":753321,"date":"2025-01-16T17:08:20","date_gmt":"2025-01-16T11:38:20","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=753321"},"modified":"2025-01-16T17:08:20","modified_gmt":"2025-01-16T11:38:20","slug":"class-11-maths-chapter-12-introduction-to-three-dimensional-geometry-mcqs","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/mcqs\/class-11-maths\/three-dimensional-geometry\/","title":{"rendered":"Class 11 Maths Chapter 12 Introduction to Three-dimensional Geometry MCQs"},"content":{"rendered":"<div class=\"flex-1 overflow-hidden @container\/thread\">\n<div class=\"h-full\">\n<div class=\"react-scroll-to-bottom--css-wvalf-79elbk h-full\">\n<div class=\"react-scroll-to-bottom--css-wvalf-1n7m0yu\">\n<div class=\"flex flex-col text-sm md:pb-9\">\n<article class=\"w-full scroll-mb-[var(--thread-trailing-height,150px)] text-token-text-primary focus-visible:outline-2 focus-visible:outline-offset-[-4px]\" dir=\"auto\" data-testid=\"conversation-turn-15\" data-scroll-anchor=\"true\">\n<div class=\"m-auto text-base py-[18px] px-3 md:px-4 w-full md:px-5 lg:px-4 xl:px-5\">\n<div class=\"mx-auto flex flex-1 gap-4 text-base md:gap-5 lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]\">\n<div class=\"group\/conversation-turn relative flex w-full min-w-0 flex-col agent-turn\">\n<div class=\"flex-col gap-1 md:gap-3\">\n<div class=\"flex max-w-full flex-col flex-grow\">\n<div class=\"min-h-8 text-message flex w-full flex-col items-end gap-2 whitespace-normal break-words text-start [.text-message+&amp;]:mt-5\" dir=\"auto\" data-message-author-role=\"assistant\" data-message-id=\"263b486e-34c1-4237-a465-09b70330ecd3\" data-message-model-slug=\"gpt-4o\">\n<div class=\"flex w-full flex-col gap-1 empty:hidden first:pt-[3px]\">\n<div class=\"markdown prose w-full break-words dark:prose-invert light\">\n<p><strong><a href=\"https:\/\/infinitylearn.com\/surge\/mcqs\/class-11-maths\/\">Class 11 Maths<\/a><\/strong> Chapter 12, &#8220;Introduction to Three-dimensional Geometry,&#8221; includes MCQs with answers available on IL. These questions are created by experienced teachers based on the latest exam pattern. The <strong><a href=\"https:\/\/infinitylearn.com\/surge\/mcqs\/\">MCQs<\/a> <\/strong>follow the <strong><a href=\"https:\/\/infinitylearn.com\/surge\/cbse\/cbse-syllabus\/\">CBSE syllabus<\/a><\/strong> (2024-2025) and<strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/\"> NCERT<\/a><\/strong> guidelines. Practicing these questions helps students understand the topic better and perform well in exams.<\/p>\n<h2>MCQs for Class 11 Maths Chapter 12 Introduction to Three-dimensional Geometry with Answers<\/h2>\n<div class=\"question\">\n<p><strong>1. The distance between the points A(x<sub>1<\/sub>, y<sub>1<\/sub>, z<sub>1<\/sub>) and B(x<sub>2<\/sub>, y<sub>2<\/sub>, z<sub>2<\/sub>) in 3D space is given by:<\/strong><\/p>\n<ol>\n<li>a) \\( \\sqrt{(x_2 &#8211; x_1)^2 + (y_2 &#8211; y_1)^2} \\)<\/li>\n<li>b) \\( (x_2 &#8211; x_1) + (y_2 &#8211; y_1) + (z_2 &#8211; z_1) \\)<\/li>\n<li>c) \\( \\sqrt{(x_2 &#8211; x_1)^2 + (y_2 &#8211; y_1)^2 + (z_2 &#8211; z_1)^2} \\)<\/li>\n<li>d) \\( \\sqrt{x_1^2 + y_1^2 + z_1^2} \\)<\/li>\n<\/ol>\n<p><strong>Answer:<\/strong> c<\/p>\n<\/div>\n<div class=\"question\">\n<p><strong>2. The coordinates of a point in space are written as:<\/strong><\/p>\n<ol>\n<li>a) (x, y)<\/li>\n<li>b) (x, y, z)<\/li>\n<li>c) (r, \u03b8)<\/li>\n<li>d) (x, z)<\/li>\n<\/ol>\n<p><strong>Answer:<\/strong> b<\/p>\n<\/div>\n<div class=\"question\">\n<p><strong>3. The distance of the point P(x, y, z) from the origin is:<\/strong><\/p>\n<ol>\n<li>a) x + y + z<\/li>\n<li>b) \\( \\sqrt{x^2 + y^2} \\)<\/li>\n<li>c) \\( \\sqrt{x^2 + y^2 + z^2} \\)<\/li>\n<li>d) z<\/li>\n<\/ol>\n<p><strong>Answer:<\/strong> c<\/p>\n<\/div>\n<div class=\"question\">\n<p><strong>4. The coordinates of the midpoint of the line segment joining A(x<sub>1<\/sub>, y<sub>1<\/sub>, z<sub>1<\/sub>) and B(x<sub>2<\/sub>, y<sub>2<\/sub>, z<sub>2<\/sub>) are:<\/strong><\/p>\n<ol>\n<li>a) \\( \\left( \\frac{x_1 + x_2}{2}, \\frac{y_1 + y_2}{2}, \\frac{z_1 + z_2}{2} \\right) \\)<\/li>\n<li>b) (x<sub>1<\/sub> + x<sub>2<\/sub>, y<sub>1<\/sub> + y<sub>2<\/sub>, z<sub>1<\/sub> + z<sub>2<\/sub>)<\/li>\n<li>c) (x<sub>2<\/sub> &#8211; x<sub>1<\/sub>, y<sub>2<\/sub> &#8211; y<sub>1<\/sub>, z<sub>2<\/sub> &#8211; z<sub>1<\/sub>)<\/li>\n<li>d) \\( \\left( \\frac{x_1 &#8211; x_2}{2}, \\frac{y_1 &#8211; y_2}{2}, \\frac{z_1 &#8211; z_2}{2} \\right) \\)<\/li>\n<\/ol>\n<p><strong>Answer:<\/strong> a<\/p>\n<\/div>\n<div class=\"question\">\n<p><strong>5. If l, m, n are the direction cosines of a line, then:<\/strong><\/p>\n<ol>\n<li>a) \\( l^2 + m^2 + n^2 = 0 \\)<\/li>\n<li>b) \\( l^2 + m^2 + n^2 = 1 \\)<\/li>\n<li>c) \\( l^2 &#8211; m^2 &#8211; n^2 = 1 \\)<\/li>\n<li>d) \\( l^2 + m^2 = 1 \\)<\/li>\n<\/ol>\n<p><strong>Answer:<\/strong> b<\/p>\n<\/div>\n<div class=\"question\">\n<p><strong>6. Which of the following represents direction ratios of a line?<\/strong><\/p>\n<ol>\n<li>a) Proportional to direction cosines<\/li>\n<li>b) Satisfies \\( l^2 + m^2 + n^2 = 1 \\)<\/li>\n<li>c) Always integers<\/li>\n<li>d) None of these<\/li>\n<\/ol>\n<p><strong>Answer:<\/strong> a<\/p>\n<\/div>\n<div class=\"question\">\n<p><strong>7. The direction cosines of a line parallel to the x-axis are:<\/strong><\/p>\n<ol>\n<li>a) (1, 0, 0)<\/li>\n<li>b) (0, 1, 0)<\/li>\n<li>c) (0, 0, 1)<\/li>\n<li>d) (1, 1, 1)<\/li>\n<\/ol>\n<p><strong>Answer:<\/strong> a<\/p>\n<\/div>\n<div class=\"question\">\n<p><strong>8. If the direction ratios of a line are 3, -6, 2, then the direction cosines are proportional to:<\/strong><\/p>\n<ol>\n<li>a) (3, -6, 2)<\/li>\n<li>b) \\( \\left( \\frac{3}{7}, \\frac{-6}{7}, \\frac{2}{7} \\right) \\)<\/li>\n<li>c) (9, 36, 4)<\/li>\n<li>d) (-3, 6, -2)<\/li>\n<\/ol>\n<p><strong>Answer:<\/strong> b<\/p>\n<\/div>\n<div class=\"question\">\n<p><strong>9. The equation of a plane passing through (x<sub>1<\/sub>, y<sub>1<\/sub>, z<sub>1<\/sub>) and normal to vector \\( \\vec{n} = \\langle a, b, c \\rangle \\) is:<\/strong><\/p>\n<ol>\n<li>a) \\( ax + by + cz + d = 0 \\)<\/li>\n<li>b) \\( a(x &#8211; x_1) + b(y &#8211; y_1) + c(z &#8211; z_1) = 0 \\)<\/li>\n<li>c) \\( ax + by + cz = d \\)<\/li>\n<li>d) \\( x + y + z = 0 \\)<\/li>\n<\/ol>\n<p><strong>Answer:<\/strong> b<\/p>\n<\/div>\n<div class=\"question\">\n<p><strong>10. A plane parallel to the xy-plane has the equation:<\/strong><\/p>\n<ol>\n<li>a) \\( z = c \\)<\/li>\n<li>b) \\( z = 0 \\)<\/li>\n<li>c) \\( x + y = 0 \\)<\/li>\n<li>d) \\( ax + by = c \\)<\/li>\n<\/ol>\n<p><strong>Answer:<\/strong> a<\/p>\n<\/div>\n<div class=\"question\"><strong>18. The plane passing through the origin and having normal vector \\( \\vec{n} = \\langle 1, -2, 3 \\rangle \\) has the equation:<\/strong><\/p>\n<ol>\n<li>a) \\( x &#8211; 2y + 3z = 0 \\)<\/li>\n<li>b) \\( x + 2y &#8211; 3z = 0 \\)<\/li>\n<li>c) \\( x &#8211; y + z = 0 \\)<\/li>\n<li>d) None of these<\/li>\n<\/ol>\n<p><strong>Answer:<\/strong> a<\/p>\n<\/div>\n<div class=\"question\"><strong>19. The distance of a point \\( P(x_1, y_1, z_1) \\) from the plane \\( ax + by + cz + d = 0 \\) is:<\/strong><\/p>\n<ol>\n<li>a) \\( \\frac{|ax_1 + by_1 + cz_1 + d|}{\\sqrt{a^2 + b^2 + c^2}} \\)<\/li>\n<li>b) \\( \\frac{ax_1 + by_1 + cz_1 + d}{\\sqrt{a^2 + b^2 + c^2}} \\)<\/li>\n<li>c) \\( \\sqrt{x_1^2 + y_1^2 + z_1^2} \\)<\/li>\n<li>d) None of these<\/li>\n<\/ol>\n<p><strong>Answer:<\/strong> a<\/p>\n<\/div>\n<div class=\"question\"><strong>20. The vector form of the equation of a plane is:<\/strong><\/p>\n<ol>\n<li>a) \\( \\vec{r} \\cdot \\vec{n} = d \\)<\/li>\n<li>b) \\( ax + by + cz + d = 0 \\)<\/li>\n<li>c) \\( \\vec{r} \\times \\vec{n} = 0 \\)<\/li>\n<li>d) None of these<\/li>\n<\/ol>\n<p><strong>Answer:<\/strong> a<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Class 11 Maths Chapter 12, &#8220;Introduction to Three-dimensional Geometry,&#8221; includes MCQs with answers available on IL. 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