Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Please solve part f and g correctly and handwritten
2. Demonstrate the following relationship involving the dot product and cross product (a) u. (v xw) = v. (w × u) = w · (u x V) (b) u. (u x v) = 0 (and explain geometrically why the result is zero) (c) (a × b) × (a × c) = [(a × b) · c]a . (d) (a × b) · (c × d) = (a · c) (b · d) — (b · c) (a · d) (e) a × (b × c) + cx (a × b) + b × (c × a) = 0 (f) ||a+b|| ≤ ||a|| + ||b|| (g) (a · b)² + ||a × b||² = ||a||²||b||².
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Transcribed Image Text:2. Demonstrate the following relationship involving the dot product and cross product (a) u. (v xw) = v. (w × u) = w · (u x V) (b) u. (u x v) = 0 (and explain geometrically why the result is zero) (c) (a × b) × (a × c) = [(a × b) · c]a . (d) (a × b) · (c × d) = (a · c) (b · d) — (b · c) (a · d) (e) a × (b × c) + cx (a × b) + b × (c × a) = 0 (f) ||a+b|| ≤ ||a|| + ||b|| (g) (a · b)² + ||a × b||² = ||a||²||b||².
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