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4. The planes , and 12 are have cartesian equations x – y+ z+1 = 0 and 2x + y – z – 1 = 0 respectively. a) Show that these two planes are not parallel. b) Find a parametric equation of their line of intersection. c) Give a Cartesian equation of plane t3 passing through point A(1, –1,–1) and perpendicular to π, and π, Given the points B(2,3, – 1) and C(4, –1,5), d) Evaluate OC.OB e) Show that OB^oċ can be expressed in the form m(OẢ), where m is a scalar. Give a geometrical interpretation of your results.

4. The planes , and 12 are have cartesian equations x – y+ z+1 = 0 and 2x + y – z – 1 = 0 respectively. a) Show that these two planes are not parallel. b) Find a parametric equation of their line of intersection. c) Give a Cartesian equation of plane t3 passing through point A(1, –1,–1) and perpendicular to π, and π, Given the points B(2,3, – 1) and C(4, –1,5), d) Evaluate OC.OB e) Show that OB^oċ can be expressed in the form m(OẢ), where m is a scalar. Give a geometrical interpretation of your results.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Solve Q4c, d & e with detailed explanations

4. The planes 1 and 1, are have cartesian equations x – y + z +1 = 0 and 2x + y – z – 1 = 0 respectively. a) Show that these two planes are not parallel. b) Find a parametric equation of their line of intersection. c) Give a Cartesian equation of plane 13 passing through point A(1, –1,–1) and perpendicular to π and πρ. Given the points B(2,3, – 1) and C(4, –1,5), d) Evaluate OC.OB e) Show that OB^OC can be expressed in the form m(0A), where m is a scalar. Give a geometrical interpretation of your results.
Transcribed Image Text:4. The planes 1 and 1, are have cartesian equations x – y + z +1 = 0 and 2x + y – z – 1 = 0 respectively. a) Show that these two planes are not parallel. b) Find a parametric equation of their line of intersection. c) Give a Cartesian equation of plane 13 passing through point A(1, –1,–1) and perpendicular to π and πρ. Given the points B(2,3, – 1) and C(4, –1,5), d) Evaluate OC.OB e) Show that OB^OC can be expressed in the form m(0A), where m is a scalar. Give a geometrical interpretation of your results.
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