Explanation 1) Concept: To solve for given identities we have to use the concept of dot product and cross product of two vectors. 2) Formulae: If a → = a x i - + a y j - + a z k - ; b - = b x i - + b y j - + b z k - Then, i. a → · b → = a x b x + a y b y + a z b z ii. a → × b → = i a y b z - a z b y - j ( a x b z - a z b x ) + k ( a x b y - a y b x ) 3) Given: i. ∣ a → ∣ = 1.4 u n i t s ii. ∣ b → ∣ = 3.20 u n i t s 4) Calculations: Vector a → lies in the yz plane 63.0 0 from the positive direction of y axis, so components will be a x = 0 a y = 3.20 × cos ⁡ 63 = 1.4527 m a z = 3.20 × sin ⁡ 63 = 2.851 m a → = a x i - + a y j - + a z k - a → = 0 i - + 1.4527 j - + 2.851 k - Vector b → lies in xz plane 48.0 0 from the positive direction of x axis, so components will be b x = 1.4 × cos ⁡ 48 = 0

10th Edition

ISBN: 9781118230718

Author: David Halliday

Publisher: Wiley, John & Sons, Incorporated

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Helmholtz Free Energy

The Helmholtz free energy is a thermodynamic potential used to calculate the measure of useful work from a closed system. This system is kept at constant temperature and volume. German physicist Hermann Helmholtz introduced this concept in 1882.

Question

Chapter 3, Problem 74P

To determine

To find:

a) a→·b→

b) a→×b→

c) The angle between a→ and b→

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Chapter 3, Problem 73P

Chapter 3, Problem 75P

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Fundamentals of Physics

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