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8 In the diagram to the right, AD and BE are altitudes of AABC intersecting at P. Let a, b, c and p be the respective position vectors of A, B, C and P relative to an origin O. a Explain why (pa) (c- b) = 0. b Explain why (pb) (ac) = 0. c Hence show that (pc) (a - b) = 0. d Deduce that the three altitudes of a triangle are concurrent. A EQ P D B

8 In the diagram to the right, AD and BE are altitudes of AABC intersecting at P. Let a, b, c and p be the respective position vectors of A, B, C and P relative to an origin O. a Explain why (pa) (c- b) = 0. b Explain why (pb) (ac) = 0. c Hence show that (pc) (a - b) = 0. d Deduce that the three altitudes of a triangle are concurrent. A EQ P D B

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8 In the diagram to the right, AD and BE are altitudes of AABC intersecting at P. Let a, b, c and p be the respective position vectors of A, B, C and P relative to an origin O. a Explain why (pa) b Explain why (p - b) c Hence show that (pc) (a - b) = 0. d Deduce that the three altitudes of a triangle are concurrent. (cb) = 0. (ac) = 0. A ED C P D B
Transcribed Image Text:8 In the diagram to the right, AD and BE are altitudes of AABC intersecting at P. Let a, b, c and p be the respective position vectors of A, B, C and P relative to an origin O. a Explain why (pa) b Explain why (p - b) c Hence show that (pc) (a - b) = 0. d Deduce that the three altitudes of a triangle are concurrent. (cb) = 0. (ac) = 0. A ED C P D B
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