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12 (a) Consider the vectors v = 6i – 2j + k and w -i+3j-2k. (i) Determine a unit vector which is perpendicular to both v and w (ii) Show that your result from (a)(ii) is perpendicular to w by calculating an appropriate scalar product. Explain your result. (iii) Determine the projection of vector v on to vector w. (h) Tue

12 (a) Consider the vectors v = 6i – 2j + k and w -i+3j-2k. (i) Determine a unit vector which is perpendicular to both v and w (ii) Show that your result from (a)(ii) is perpendicular to w by calculating an appropriate scalar product. Explain your result. (iii) Determine the projection of vector v on to vector w. (h) Tue

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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solve all parts of (a)
12 (a) Consider the vectors v = 6i – 2j + k and w = -i+3j- 2k. (i) Determine a unit vector which is perpendicular to both v and w (ii) Show that your result from (a)(ii) is perpendicular to w by calculating an appropriate scalar product. Explain your result. (iii) Determine the projection of vector v on to vector w. (b) Two out-of-phase alternating voltages are represented by: V = 3.4sin (wt +) and V, = 1.3cos (wt +). %3D %3D By representing these phasors as vectors, use vector addition to find the sum of V, and V½ in the form A sin(@t + )
Transcribed Image Text:12 (a) Consider the vectors v = 6i – 2j + k and w = -i+3j- 2k. (i) Determine a unit vector which is perpendicular to both v and w (ii) Show that your result from (a)(ii) is perpendicular to w by calculating an appropriate scalar product. Explain your result. (iii) Determine the projection of vector v on to vector w. (b) Two out-of-phase alternating voltages are represented by: V = 3.4sin (wt +) and V, = 1.3cos (wt +). %3D %3D By representing these phasors as vectors, use vector addition to find the sum of V, and V½ in the form A sin(@t + )
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