ISM_T11_C12_B - Section 12.5 Lines and Planes in Space â j...

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Section 12.5 Lines and Planes in Space 801 37. S(3 1 4), P(4 3 5) and 2 3 PS 30 6 6 1 4 9 1 2 3 ß ß ß ß œ Ê œ œ Ä v i j k v i j k i j k â â â â â â â â â â â â d is the distance from S to the line Ê œ œ œ œ œ œ ¹ ¹ k k È È È È È È È È È PS 900 36 36 1 4 9 972 486 81 6 14 7 7 9 42 7 Ä v v 38. S( 1 4 3), P(10 3 0) and 4 4 PS 28 56 28 28( 2 ) 11 7 3 4 0 4 ß ß ß ß œ Ê œ œ œ Ä v i k v i j k i j k i j k â â â â â â â â â â â â d 7 3 is the distance from S to the line Ê œ œ œ ¹ ¹ k k È È PS 28 1 4 1 4 1 1 Ä v v È 39. S(2 3 4), x 2y 2z 13 and P(13 0 0) is on the plane PS 11 3 4 and 2 2 ß ß œ ß ß Ê œ œ Ä i j k n i j k d PS 3 Ê œ œ œ œ Ä ¹ ¹ ¹ ¹ ¹ ¹ n n k k È È 11 6 8 9 1 4 4 9 40. S(0 0 0), 3x 2y 6z 6 and P(2 0 0) is on the plane PS 2 and 3 2 6 ß ß œ ß ß Ê œ œ Ä i n i j k d PS Ê œ œ œ œ Ä ¹ ¹ ¹ ¹ n n k k È È 6 6 6 9 4 36 49 7 41. S(0 1 1), 4y 3z 12 and P(0 3 0) is on the plane PS 4 and 4 3 ß ß œ ß ß Ê œ œ Ä j k n j k d PS Ê œ œ œ Ä ¹ ¹ ¹ ¹ n n k k È 16 3 19 16 9 5 42. S(2 2 3), 2x y 2z 4 and P(2 0 0) is on the plane PS 2 3 and 2 2 ß ß œ ß ß Ê œ œ Ä j k n i j k d PS Ê œ œ œ Ä ¹ ¹ ¹ ¹ n n k k È 2 6 8 4 1 4 3 43. S(0 1 0), 2x y 2z 4 and P(2 0 0) is on the plane PS 2 and 2 2 ß ß œ ß ß Ê œ œ Ä i j n i j k d PS Ê œ œ œ Ä ¹ ¹ ¹ ¹ n n k k È 4 1 0 5 4 1 4 3 44. S(1 0 1), 4x y z 4 and P( 1 0 0) is on the plane PS 2 and 4 ß ß œ ß ß Ê œ œ Ä i k n i j k d PS Ê œ œ œ œ Ä ¹ ¹ ¹ ¹ n n k k È È È # 8 1 9 16 1 1 18 3 2 45. The point P(1 0 0) is on the first plane and S(10 0 0) is a point on the second plane PS 9 , and ß ß ß ß Ê œ Ä i 2 6 is normal to the first plane the distance from S to the first plane is d PS n i j k œ Ê œ Ä ¹ ¹ n n k k , which is also the distance between the planes. œ œ ¹ ¹ 9 9 1 4 36 41 È È 46. The line is parallel to the plane since ( 2 6 ) 1 2 3 0. Also the point v n i j k i j k œ œ œ ˆ " # S(1 0 0) when t 1 lies on the line, and the point P(10 0 0) lies on the plane PS 9 . The distance ß ß œ ß ß Ê œ Ä i from S to the plane is d PS , which is also the distance from the line to the œ œ œ Ä ¹ ¹ ¹ ¹ n n k k È È 9 9 1 4 36 41 plane.
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