{"id":4623,"date":"2016-05-17T11:49:00","date_gmt":"2016-05-17T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-12-2\/"},"modified":"2016-05-17T12:09:42","modified_gmt":"2016-05-17T06:39:42","slug":"ncert-solutions-class-11-maths-exercise-12-2","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-12-2\/","title":{"rendered":"NCERT Solutions class-11 Maths Exercise 12.2"},"content":{"rendered":"

Exercise 12.2<\/strong><\/p>\n

1. Find the distance between the following pairs of points:<\/strong><\/p>\n

(i) (2, 3, 5) and (4, 3, 1) <\/strong><\/p>\n

(ii) and <\/strong><\/p>\n

(iii) and <\/strong><\/p>\n

(iv) and <\/strong><\/p>\n

Ans. (i)<\/strong> Let A (2, 3, 5) and B (4, 3, 1) be two points, then<\/p>\n

AB = <\/p>\n

= = units<\/p>\n

(ii)<\/strong> Let A (\u20133, 7, 2) and B (2, 4, \u20131) be two points, then<\/p>\n

AB = <\/p>\n

= = units<\/p>\n

(iii)<\/strong> Let A (\u20131, 3, \u20134) and B (1, \u20133, 4) be two points, then<\/p>\n

AB = <\/p>\n

= = units<\/p>\n

(iv)<\/strong> Let A (2, \u20131, 3) and B (\u20132, 1, 3) be two points, then<\/p>\n

AB = <\/p>\n

= = units<\/p>\n

\n

2. Show that the points <\/strong> and <\/strong> are collinear.<\/strong><\/p>\n

Ans. <\/strong>Let A (\u20132, 3, 5), B (1, 2, 3) and C (7, 0, \u20131) be three points, then<\/p>\n

AB = <\/p>\n

= = units<\/p>\n

BC = <\/p>\n

= = units<\/p>\n

AC = = <\/p>\n

= = units<\/p>\n

Here, AC = AB + BC<\/p>\n

Therefore A, B and C are collinear.<\/p>\n

\n

3. Verify the following:<\/strong><\/p>\n

(i) <\/strong> and <\/strong> are the vertices of an isosceles triangle.<\/strong><\/p>\n

(ii) <\/strong> and <\/strong> are the vertices of right angled triangle.<\/strong><\/p>\n

(iii) <\/strong> and <\/strong> are the vertices of a parallelogram.<\/strong><\/p>\n

Ans. (i)<\/strong> Let A (0, 7, \u201310) B (1, 6, \u20136) and C (4, 9, \u20136) be three vertices of , then<\/p>\n

AB = <\/p>\n

= = units<\/p>\n

BC = <\/p>\n

= = units<\/p>\n

AC = = <\/p>\n

= = units<\/p>\n

Here, AB = BC<\/p>\n

Therefore is an isosceles triangle.<\/p>\n

(ii)<\/strong> Let A (\u20131, 2, 1), B (\u20131, 6, 6) and C (\u20134, 9, 6) be three vertices of , then<\/p>\n

AB = <\/p>\n

= = units<\/p>\n

BC = <\/p>\n

= = units<\/p>\n

AC = = <\/p>\n

= = units<\/p>\n

Here, AC2<\/sup> = AB2<\/sup> + BC2<\/sup><\/p>\n

Therefore is a right angled triangle.<\/p>\n

(iii)<\/strong> Let A (0, 7, 10), B (1, \u20132, 5), C (4, \u20137, 8) and D (2, \u20133, 4) be four vertices of a quadrilateral ABCD, then<\/p>\n

AB = <\/p>\n

= = units<\/p>\n

BC = <\/p>\n

= = units<\/p>\n

CD = <\/p>\n

= = units<\/p>\n

AD = <\/p>\n

= = units<\/p>\n

AC = <\/p>\n

= = units<\/p>\n

BD = <\/p>\n

= = units<\/p>\n

Here, AB = CD, BC = AD and AC BD<\/p>\n

Therefore A, B, C and are the vertices of a parallelogram ABCD.<\/p>\n

\n

4. Find the equation of the set of points which are equidistant from the point (1, 2, 3) and <\/strong><\/p>\n

Ans. <\/strong>Let A be any point which is equidistant from points B (1, 2, 3) and C Then<\/p>\n

According to question, AB = AC<\/p>\n

<\/p>\n

Squaring both sides, we get<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

5. Find the equation of the set of points P, the sum of whose distance from A (4, 0, 0) and B<\/strong> is equal to 10.<\/strong><\/p>\n

Ans. <\/strong>Let P be any point, then<\/p>\n

According to question, PA + PB = 10<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

Squaring both sides, we get<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

Again squaring both sides, we get<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

This is the required equation.<\/p>\n","protected":false},"excerpt":{"rendered":"

Exercise 12.2 1. Find the distance between the following pairs of points: (i) (2, 3, 5) and (4, 3, 1) (ii) and (iii) and (iv) and Ans. (i) Let A (2, 3, 5) and B (4, 3, 1) be two points, then AB = = = units (ii) Let A (\u20133, 7, 2) and B … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[47,281],"tags":[],"class_list":["post-4623","post","type-post","status-publish","format-standard","hentry","category-cbse-class-11","category-ncert-solutions"],"yoast_head":"\nNCERT Solutions class-11 Maths Exercise 12.2 | myCBSEguide<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-12-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions class-11 Maths Exercise 12.2 | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"Exercise 12.2 1. Find the distance between the following pairs of points: (i) (2, 3, 5) and (4, 3, 1) (ii) and (iii) and (iv) and Ans. (i) Let A (2, 3, 5) and B (4, 3, 1) be two points, then AB = = = units (ii) Let A (\u20133, 7, 2) and B ... 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