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 14 9 123 ß± ß ß ß± œ± ² ² Ê ‚ œ œ± ± ± Ä ±± ± v ijk v ij k ââ d is the distance from S to the line Ê œ œ œœœ œ ¹¹ kk È ÈÈÈ È ÈÈ È È PS 900 36 36 149 972 486 81 6 14 77 94 2 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 40 4 ±ßß ß±ß œ ² Ê œ ² ± œ ² ± Ä ± vik v i j k k k d 7 3 is the distance from S to the line Êœ œ œ È È PS 2 8141 411 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 ²²œ ß ß Ê œ ±±² œ²² Ä n dP S 3 œ œ œ Ä ¹ ¹ ¹ ¹ n n ²²± ² 1 168 9 144 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 ßß ² ² œ Ê œ± œ ² ² Ä ini j k S œ Ä ¹ ¹ n n ² 66 6 943 6 49 7 41. S(0 1 1), 4y 3z 12 and P(0 3 0) is on the plane PS 4 and 4 3 ² œ± Ê œ ² Ä jk n j k S œ œ Ä ¹ ¹ n n 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 Ê œ ²² Ä jk ni S œ œ Ä ¹ ¹ n n È 26 8 414 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 Ê œ± ± Ä ij n ij k S œ œ Ä ¹ ¹ n n È 410 5 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 ± ± ²²œ ± ß ß Ê œ ± œ±²² Ä ik n S œ Ä ¹ ¹ n n È ²² # 81 9 1 611 18 32 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 Ê œ Ä i 2 6 is normal to the first plane the distance from S to the first plane is d PS ni j k œ² ² Ê œ Ä n n , which is also the distance between the planes. œœ 99 143 6 41 46. The line is parallel to the plane since ( 2 6 ) 1 2 3 0. Also the point vn i j k i j k †† œ²± ²² œ²±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 Ê Ä i from S to the plane is d PS , which is also the distance from the line to the œ Ä ¹ ¹ n n ² 6 41 plane. 47. and 2 2 cos cos cos j n i "# ²" ²" ²" ±" œ² œ ²± Ê œ œ œ œ ) Š‹ Š nn È 4 21 2 9 2 1
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802 Chapter 12 Vectors and the Geometry of Space 48. 5 and 2 3 cos cos cos (0) ni j k n i j k "# ±" ±" ±" ±± # œ±² œ²± Êœ œ œ œ ) Š‹ Š nn kk È È 523 27 14 1 49. 2 2 2 and 2 2 cos cos cos 1.76 rad j k j k ±" ±" ±" ± " œ±± œ²²Êœ œ œ ¸ ) Š Š ÈÈ È 442 12 9 33 50. and cos cos 0.96 rad j k nk ±" ±" œ Ê œ œ ¸ ) È È 1 3 1 51. 2 2 and 2 cos cos cos 0.82 rad n i jk n i jk ±" ±" ±" ²± œ±±Êœ œ œ ¸ ) Š Š È 241 5 9 6 3 6 52. 4 3 and 3 2 6 cos cos cos 0.73 rad
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ISM_T11_C12_B - Section 12.5 Lines and Planes in Space â j...

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