Questions from General Calculus


Q: Prove that /

Prove that

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Q: Suppose that a ± 0. (a). If a

Suppose that a ± 0. (a). If a ∙ b = a ∙ c, does it follow that b = c? (b). If a × b = a × c, does it follow that b = c? (c). If a ∙ b = a ∙ c and a × b = a × c, does it follow that b = c?

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Q: If v1, v2, and v3 are non-coplanar vectors

If v1, v2, and v3 are non-coplanar vectors, let (These vectors occur in the study of crystallography. Vectors of the form n1v1 + n2v2 + n3v3, where each ni is an integer, form a lattice for a crysta...

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Q: Let L1 be the line through the origin and the point (

Let L1 be the line through the origin and the point (2, 0, -1). Let L2 be the line through the points (1, -1, 1) and (4, 1, 3). Find the distance between L1 and L2.

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Q: Show that the curve y = 2ex + 3x + 5x3 has

Show that the curve y = 2ex + 3x + 5x3 has no tangent line with slope 2.

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Q: Let L1 be the line through the points (1, 2

Let L1 be the line through the points (1, 2, 6) and (2, 4, 8). Let L2 be the line of intersection of the planes P1 and P2, where P1 is the plane x - y + 2z + 1 = 0 and P2 is the plane through the poin...

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Q: Two tanks are participating in a battle simulation. Tank A is

Two tanks are participating in a battle simulation. Tank A is at point (325, 810, 561) and tank B is positioned at point (765, 675, 599). (a). Find parametric equations for the line of sight between...

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Q: Find parametric equations and symmetric equations for the line. The

Find parametric equations and symmetric equations for the line. The line through the points (-8, 1, 4) and (3, -2, 4)

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Q: Find parametric equations and symmetric equations for the line. The

Find parametric equations and symmetric equations for the line. The line through (2, 1, 0) and perpendicular to both i + j and j + k

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Q: Find parametric equations and symmetric equations for the line. The

Find parametric equations and symmetric equations for the line. The line of intersection of the planes x + -y + 3z = 1 and x - y + z = 1

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