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Chapter 10: Vectors and the geometry of space

Expert-verified
Essential Calculus: Early Transcendentals
Pages: 537 - 614
Essential Calculus: Early Transcendentals

Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

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Illustration

507 Questions for Chapter 10: Vectors and the geometry of space

  1. (a) Find and identify the traces of the quadric surface \( - {x^2} - {y^2} + {z^2} = 1\) and explain why the graph looks like the graph of the hyperboloid of two sheets in Table \(1\).

    Found on Page 579

  2. Determine the sum of two vectors.

    Found on Page 549

  3. Reparametrize the curve with respect to arc length measured from the point where t=0 in the direction of increasing t.

    Found on Page 598

  4. Find an equation of a sphere with center\({\rm{(2, - 6,4)}}\) and radius\({\rm{5}}\) and describe the intersection of the sphere with the\({\rm{xy - }}\)plane, \({\rm{yz - }}\)plane and\({\rm{xz - }}\)plane.

    Found on Page 541

  5. Sketch the curve with the given vector equation. Indicate with an arrow the direction in which increases.

    Found on Page 589

  6. Find the velocity, acceleration, and speed of a particle with the given position function.

    Found on Page 608

  7. To find a dot product between \({\rm{a}}\) and \({\rm{b}}\).

    Found on Page 556

  8. Find the parametric equations for the line of intersection of the planes \(x + 2y + 3z = 1\) and \(x - y + z = 1\) and the symmetric equations for the line of intersection of the planes \(x + 2y + 3z = 1\) and \(x - y + z = 1\).

    Found on Page 572

  9. Find the resultant vector of \({\rm{k}} \times ({\rm{i}} - 2{\rm{j}})\) using cross product.

    Found on Page 564

  10. Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

    Found on Page 611

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