{"id":21303,"date":"2020-01-24T16:09:07","date_gmt":"2020-01-24T10:39:07","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=21303"},"modified":"2021-07-02T15:27:04","modified_gmt":"2021-07-02T09:57:04","slug":"2nd-puc-maths-question-bank-chapter-11-ex-11-1","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-maths-question-bank-chapter-11-ex-11-1\/","title":{"rendered":"2nd PUC Maths Question Bank Chapter 11 Three Dimensional Geometry Ex 11.1"},"content":{"rendered":"

Students can Download Maths Chapter 11 Three Dimensional Geometry Ex 11.1 Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers<\/a>\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n

Karnataka 2nd PUC Maths Question Bank Chapter 11 Three Dimensional Geometry Ex 11.1<\/h2>\n

2nd PUC Maths Three Dimensional Geometry NCERT Text Book Questions and Answers\u00a0Ex 11.1<\/h3>\n

Question 1.
\nIf a line makes angles 90\u00b0, 135\u00b0, 45\u00b0 with the x, y and z-axes respectively, find its direction cosines.
\nAnswer:
\nDc\u2019s are cos \u03b1, cos \u03b2 and cos \u03b3
\ncos 90\u00b0, cos 135\u00b0, cos 45\u00b0
\n\\(\\left(0, \\frac{-1}{\\sqrt{2}}, \\frac{1}{\\sqrt{2}}\\right)\\)<\/p>\n

Question 2.
\nFind the direction cosines of a line which makes equal angles with the coordinate axes.
\nAnswer:
\nLet the angle be \u03b1,\u03b1,\u03b1
\nDirection cosines are cos \u03b1, cos \u03b1 , cos \u03b1
\nbut cos2<\/sup> \u03b1 + cos2<\/sup> \u03b22<\/sup> + cos2<\/sup> \u03b3 = 1
\ncos2<\/sup> \u03b1 + cos2<\/sup> \u03b1+ cos2<\/sup>\u00a0\u03b1 = 1 \u21d2 3cos2<\/sup>\u00a0\u03b1= 1
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 3.
\nIf a line has the direction ratios -18, 12, – 4, then what are its direction cosines ?
\nAnswer:
\na : b : c = -18 : 12 : -4
\nlet l1<\/sub>, m1<\/sub>, n are the dc\u2019s
\n\"2nd<\/p>\n

Question 4.
\nShow that the points (2, 3, 4), (- 1, – 2, 1), (5, 8, 7) are collinear.
\nAnswer:
\nLet A (2, 3, 4), B (-1, -2, 1) C (5, 8, 7)
\nDirections of AB = (-1 -2, -2 -3, +1, – 4) =(-3, -5, -3)
\nDr\u2019s of AC = (5-2, 8-3, 7-4) = (3, 5, 3)
\nDr\u2019 of AB and AC are proportional.
\nHence AB and AC are parallel. But A is common
\n\u2234 points A, B, C are collinear<\/p>\n

\"KSEEB<\/p>\n

Question 5.
\nFind the direction cosines of the sides of the triangle whose vertices are
\n(3, 5, – 4), (- 1, 1, 2) and (- 5, – 5, – 2).
\nAnswer:
\nLet (3,5, -4), B (-1,1,2) and C (-5, -5, -2) Dr\u2019 of
\nAB = (-4, -4, 6), Dc\u2019s AB =
\n\"2nd<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Maths Chapter 11 Three Dimensional Geometry Ex 11.1 Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka 2nd PUC Maths Question Bank Chapter 11 Three Dimensional Geometry Ex 11.1 2nd PUC Maths …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[82],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/21303"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=21303"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/21303\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=21303"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=21303"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=21303"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}