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(a) Evaluate the scalar product (i) (1-i, 15, -40) · (15,6 +3i, ) and the vector products (ii) (4, -4,4) × (3, -10,5) and (12, -3,5) × ((4, 0, 1) × (3, 1,0)). (b) Find the equation of the plane which contains the points (2, 1, -1), (0, -2,0) and (1,-1,2) (c) A force F = (5,5,-2) acts on a body that moves from the point (-4, 3, 1) to the point (7, 8, 6). Find the displacement r of the body and the work W done

(a) Evaluate the scalar product (i) (1-i, 15, -40) · (15,6 +3i, ) and the vector products (ii) (4, -4,4) × (3, -10,5) and (12, -3,5) × ((4, 0, 1) × (3, 1,0)). (b) Find the equation of the plane which contains the points (2, 1, -1), (0, -2,0) and (1,-1,2) (c) A force F = (5,5,-2) acts on a body that moves from the point (-4, 3, 1) to the point (7, 8, 6). Find the displacement r of the body and the work W done

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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(a) Evaluate the scalar product (i) (1-i, 15, -40) · (15,6 +3i, §) and the vector products (ii) (4, -4,4) × (3, -10,5) and (12, −3, 5) × ((4, 0, 1) × (3, 1, 0)). (b) Find the equation of the plane which contains the points (2, 1,−1), (0, -2, 0) and (1,-1,2) (c) A force F = (5, 5, -2) acts on a body that moves from the point (-4, 3, 1) to the point (7, 8, 6). Find the displacement r of the body and the work W done by the force. Determine the angle between the force and the displacement.
Transcribed Image Text:(a) Evaluate the scalar product (i) (1-i, 15, -40) · (15,6 +3i, §) and the vector products (ii) (4, -4,4) × (3, -10,5) and (12, −3, 5) × ((4, 0, 1) × (3, 1, 0)). (b) Find the equation of the plane which contains the points (2, 1,−1), (0, -2, 0) and (1,-1,2) (c) A force F = (5, 5, -2) acts on a body that moves from the point (-4, 3, 1) to the point (7, 8, 6). Find the displacement r of the body and the work W done by the force. Determine the angle between the force and the displacement.
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