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The points A and B have position vectors, relative to the origin O, given by OA = i+ 2j + 3k and OB = 2i +j+ 3k. The line I has vector equation r = (1 – 21)i + (5 + t)j + (2 – t)k. (i) Show that I does not intersect the line passing through A and B. (ii) The point P lies on l and is such that angle PAB is equal to 60°. Given that the position vector ofP is (1- 2t)i + (5 + t)j + (2 – t)k, show that 3t2 + 7t+2 0. Hence find the only possible position vector of P.

The points A and B have position vectors, relative to the origin O, given by OA = i+ 2j + 3k and OB = 2i +j+ 3k. The line I has vector equation r = (1 – 21)i + (5 + t)j + (2 – t)k. (i) Show that I does not intersect the line passing through A and B. (ii) The point P lies on l and is such that angle PAB is equal to 60°. Given that the position vector ofP is (1- 2t)i + (5 + t)j + (2 – t)k, show that 3t2 + 7t+2 0. Hence find the only possible position vector of P.

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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10 The points A and B have position vectors, relative to the origin O, given by OA = i+ 2j + 3k and OB = 2i +j+ 3k. The line I has vector equation 3(1-20)i + (5 + oj+ (2 – t)k. (i) Show that I does not intersect the line passing through A and B. (ii) The point P lies on I and is such that angle PAB is equal to 60°. Given that the position vector of P is (1- 20)i + (5+ t)j + (2 – t)k, show that 3t2 +7t+2 0. Hence find the only possible position vector of P. n atiou al 4S & 4 I cucl MMathematics
Transcribed Image Text:10 The points A and B have position vectors, relative to the origin O, given by OA = i+ 2j + 3k and OB = 2i +j+ 3k. The line I has vector equation 3(1-20)i + (5 + oj+ (2 – t)k. (i) Show that I does not intersect the line passing through A and B. (ii) The point P lies on I and is such that angle PAB is equal to 60°. Given that the position vector of P is (1- 20)i + (5+ t)j + (2 – t)k, show that 3t2 +7t+2 0. Hence find the only possible position vector of P. n atiou al 4S & 4 I cucl MMathematics
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