{"id":4625,"date":"2016-05-17T11:49:00","date_gmt":"2016-05-17T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-4\/"},"modified":"2016-05-17T12:11:32","modified_gmt":"2016-05-17T06:41:32","slug":"ncert-solutions-class-11-maths-miscellaneous-10","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-miscellaneous-10\/","title":{"rendered":"NCERT Solutions class-11 Maths Miscellaneous"},"content":{"rendered":"

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

1. Three vertices of a parallelogram ABCD are A<\/strong> B<\/strong> and C<\/strong> Find the coordinates of the fourth vertex.<\/strong><\/p>\n

Ans. <\/strong>Let D be the fourth vertex of parallelogram ABCD.<\/p>\n

<\/p>\n

Since, the diagonals of a parallelogram bisect each other. Therefore, the mid-point of AAAC and BD coincide.<\/p>\n

Coordinates of mid-point of AC<\/p>\n

= = <\/p>\n

Also Coordinates of mid-point of<\/p>\n

BD = <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

Therefore, the coordinates of point D are <\/p>\n

\n

2. Find the length of the medians of the triangle with vertices A (0, 0, 6), B (0, 4, 0) and C (6, 0, 0).<\/strong><\/p>\n

Ans. <\/strong>Given: A (0, 0, 6), B (0, 4, 0) and C (6, 0, 0) are vertices of <\/p>\n

Let D, E and F be the mid-points of BC, AC and AB respectively. Then<\/p>\n

Coordinates of D = = <\/p>\n

And AD = units<\/p>\n

Again, Coordinates of E = = <\/p>\n

And BE = units<\/p>\n

Also Coordinates of F = = <\/p>\n

And CF = units<\/p>\n

\n

3. If the origin is the centroid of the triangle PQR with vertices P<\/strong> Q<\/strong> and R<\/strong> then find the values of <\/strong> and <\/strong><\/p>\n

Ans. <\/strong>Given: P Q and R are the vertices of triangle PQR.<\/p>\n

Coordinates of centroid of = <\/p>\n

= <\/p>\n

According to question,<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

Therefore, , , <\/p>\n

\n

4. Find the coordinates of a point on <\/strong>axis which are at a distance of <\/strong> from the point P<\/strong><\/p>\n

Ans. <\/strong>Let Q be any point on axis. Then according to question,<\/p>\n

PQ = = <\/p>\n

<\/p>\n

<\/p>\n

Squaring both sides,<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

Therefore, the coordinates of point Q are (0, 2, 0) and <\/p>\n

\n

5. A point R with <\/strong>coordinate 4 lies on the line segment joining the points P<\/strong> and Q (8, 0, 10). Find the coordinates of the point R.<\/strong><\/p>\n

Ans. <\/strong>Let R be any point which divides the line segment joining P and Q in the ratio internally.<\/p>\n

Coordinates of R = <\/p>\n

But according to question, <\/p>\n

<\/p>\n

and <\/p>\n

Therefore, coordinates of R is <\/p>\n

\n

6. If A and B be the points (3, 4, 5) and <\/strong> respectively. Find the equation of the set of points P such that <\/strong> where <\/strong> is a constant.<\/strong><\/p>\n

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

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Miscellaneous Exercise 1. Three vertices of a parallelogram ABCD are A B and C Find the coordinates of the fourth vertex. Ans. Let D be the fourth vertex of parallelogram ABCD. Since, the diagonals of a parallelogram bisect each other. Therefore, the mid-point of AAAC and BD coincide. Coordinates of mid-point of AC = = … 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-4625","post","type-post","status-publish","format-standard","hentry","category-cbse-class-11","category-ncert-solutions"],"yoast_head":"\nNCERT Solutions class-11 Maths Miscellaneous | 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-miscellaneous-10\/\" \/>\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 Miscellaneous | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"Miscellaneous Exercise 1. Three vertices of a parallelogram ABCD are A B and C Find the coordinates of the fourth vertex. Ans. Let D be the fourth vertex of parallelogram ABCD. Since, the diagonals of a parallelogram bisect each other. Therefore, the mid-point of AAAC and BD coincide. Coordinates of mid-point of AC = = ... 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