Questions from General Calculus


Q: If a child pulls a sled through the snow on a level

If a child pulls a sled through the snow on a level path with a force of 50 N exerted at an angle of 380 above the horizontal, find the horizontal and vertical components of the force.

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Q: If c = |a |b + |b |a

If c = |a |b + |b |a, where a, b, and c are all nonzero vectors, show that c bisects the angle between a and b.

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Q: The gas law for an ideal gas at absolute temperature T (

The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the number of moles of the gas and R = 0.0821 is the...

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Q: Prove Properties 2, 4, and 5 of the dot product

Prove Properties 2, 4, and 5 of the dot product (Theorem 2).

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Q: The Triangle Inequality for vectors is / (

The Triangle Inequality for vectors is (a). Give a geometric interpretation of the Triangle Inequality. (b). Use the Cauchy-Schwarz Inequality from Exercise 61 to prove the Triangle Inequality. [Hin...

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Q: The Parallelogram Law states that / (a

The Parallelogram Law states that (a). Give a geometric interpretation of the Parallelogram Law. (b). Prove the Parallelogram Law.

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Q: Show that if u + v and u - v are orthogonal

Show that if u + v and u - v are orthogonal, then the vectors u and v must have the same length.

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Q: Find a ∙ b. a = 2i + j,

Find a ∙ b. a = 2i + j, b = i - j + k

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Q: Find a ∙ b. a = 3i + 2j -

Find a ∙ b. a = 3i + 2j - k, b = 4i + 5k

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Q: Find a ∙ b. |a | = 7,

Find a ∙ b. |a | = 7, |b | = 4, the angle between a and b is 30°

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