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Consider the vectors a = 6i + 7j + 6k and b = 4i – j+ 8k, where i, j, and k are mutually- perpendicular unit vectors forming a right-handed system. (a) Calculate (i) a + b. (ii) The magnitude |a| of a. (iii) The unit vector b in the direction of b. (iv) The scalar product a · b. (v) The vector product a x b. (vi) The direction cosines of a. (vii) The angle between a and b, expressed in degrees to two decimal places.

Consider the vectors a = 6i + 7j + 6k and b = 4i – j+ 8k, where i, j, and k are mutually- perpendicular unit vectors forming a right-handed system. (a) Calculate (i) a + b. (ii) The magnitude |a| of a. (iii) The unit vector b in the direction of b. (iv) The scalar product a · b. (v) The vector product a x b. (vi) The direction cosines of a. (vii) The angle between a and b, expressed in degrees to two decimal places.

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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Consider the vectors a = 6i + 7j + 6k and b = 4i – j+ 8k, where i, j, and k are mutually- perpendicular unit vectors forming a right-handed system. (a) Calculate (i) a + b. (ii) The magnitude |a| of a. (iii) The unit vector 6 in the direction of b. (iv) The scalar product a · b. (v) The vector product a x b. (vi) The direction cosines of a. (vii) The angle between a and b, expressed in degrees to two decimal places. (b) (i) If c = cİ+ Czj + 12k is parallel to the vector a above, determine the values of c %3D and c2. (ii) If d = d,i+ 12j + dzk is perpendicular to both a and b above, determine the values of di and dz. (c) Four non-coplanar points A, B, C, D are positioned such that the line AB is perpendic- ular to CD, and BC is perpendicular to AD. Using vector methods, show that AC is perpendicular to BD.
Transcribed Image Text:Consider the vectors a = 6i + 7j + 6k and b = 4i – j+ 8k, where i, j, and k are mutually- perpendicular unit vectors forming a right-handed system. (a) Calculate (i) a + b. (ii) The magnitude |a| of a. (iii) The unit vector 6 in the direction of b. (iv) The scalar product a · b. (v) The vector product a x b. (vi) The direction cosines of a. (vii) The angle between a and b, expressed in degrees to two decimal places. (b) (i) If c = cİ+ Czj + 12k is parallel to the vector a above, determine the values of c %3D and c2. (ii) If d = d,i+ 12j + dzk is perpendicular to both a and b above, determine the values of di and dz. (c) Four non-coplanar points A, B, C, D are positioned such that the line AB is perpendic- ular to CD, and BC is perpendicular to AD. Using vector methods, show that AC is perpendicular to BD.
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