(a) Consider the vectors a - -2i + 10j + 11k and b - 1i - 2j + 2k, where i, j, and k are mutually-perpendicular unit vectors forming a right-handed system. Calculate: (b) Let the vectors a and b in part (a) of this question represent the position vectors of a 2 kg point mass and a 4 kg point mass respectively (where the units of distance are considered to be subsumed within i, j, and k). Calculate where a third point mass of 3 kg would need to be positioned to make the centre of mass of the system lie at the origin. (c) Prove, by writing out in component form, that ) c (e x d) - 0. (i) (c x d) xe - (c e)d - (d-e)c.

(a) Consider the vectors a - -2i + 10j + 11k and b - 1i - 2j + 2k, where i, j, and k are mutually-perpendicular unit vectors forming a right-handed system. Calculate: (b) Let the vectors a and b in part (a) of this question represent the position vectors of a 2 kg point mass and a 4 kg point mass respectively (where the units of distance are considered to be subsumed within i, j, and k). Calculate where a third point mass of 3 kg would need to be positioned to make the centre of mass of the system lie at the origin. (c) Prove, by writing out in component form, that ) c (e x d) - 0. (i) (c x d) xe - (c e)d - (d-e)c.

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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