Questions from General Calculus


Q: If the vectors in the figure satisfy |u| − |

If the vectors in the figure satisfy |u| − |v| = 1 and u + v + w = 0, what is |w|?

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Q: Find the lengths of the sides of the triangle PQR. Is

Find the lengths of the sides of the triangle PQR. Is it a right triangle? Is it an isosceles triangle? P (2, -1, 0), Q (4, 1, 1), R (4, -5, 4).

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Q: Refer to the law of laminar flow given in Example 7.

Refer to the law of laminar flow given in Example 7. Consider a blood vessel with radius 0.01 cm, length 3 cm, pressure difference 3000 dynes/cm2, and viscosity = 0.027. (a) Find the velocity of the...

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Q: Find an equation of the sphere that passes through the point (

Find an equation of the sphere that passes through the point (4, 3, -1) and has center (3, 8, 1).

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Q: Find an equation of the sphere that passes through the origin and

Find an equation of the sphere that passes through the origin and whose center is (1, 2, 3).

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Q: Find the sum of the given vectors and illustrate geometrically.

Find the sum of the given vectors and illustrate geometrically. 3, 0, 1 , 0, 8, 0

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Q: Find the sum of the given vectors and illustrate geometrically.

Find the sum of the given vectors and illustrate geometrically. 1, 3, −2 , 0, 0, 6

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Q: Show that the equation represents a sphere, and find its center

Show that the equation represents a sphere, and find its center and radius. 2x2 + 2y2 + 2z2 = 8x - 24z + 1

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Q: Show that the equation represents a sphere, and find its center

Show that the equation represents a sphere, and find its center and radius. 3x2 + 3y2 + 3z2 = 10 + 6y + 12z

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Q: Find dy/dx by implicit differentiation. xey = x

Find dy/dx by implicit differentiation. xey = x - y

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