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Chapter 10: Q .9. (page 834)

Find an equation of the line containing the point $(- 1, 3, 7)$ with direction vector $(2, - 4, 9)$ .
(a) Use a different direction vector to find another equation for the same line. (b) Find an equation for the same line with the form
$x = a t + 5, y = b t + y_{0}, z = c t + z_{0} .$

Short Answer

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Part a)

Part b)

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Most popular questions from this chapter

Use the Intermediate Value Theorem to prove that every cubic function $f (x) = A x^{3} + B x^{2} + C x + D$ has at least one real root. You will have to first argue that you can find real numbers a and b so that f(a) is negative and f(b) is positive.

In Exercises 30–35 compute the indicated quantities when $u = (- 3, 1, - 4), v = (2, 0, 5), and w = (1, 3, 13)$

Find the volume of the parallelepiped determined by the vectors u, v, and w.

Find $\vec{P Q}$

$P = (- 1, 5, 4), Q = (- 1, 6, 4)$

If $||u \times v|| = ||u|| ||v||$ , what is the geometric relationship between u and v?

In Exercises 30–35 compute the indicated quantities when

$u = (- 3, 1, - 4), v = (2, 0, 5), and w = (1, 3, 13)$

$u \times v and v \times u$

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Find an equation of the line containing the point $(- 1, 3, 7)$ with direction vector $(2, - 4, 9)$ .
(a) Use a different direction vector to find another equation for the same line. (b) Find an equation for the same line with the form
$x = a t + 5, y = b t + y_{0}, z = c t + z_{0} .$

Short Answer

Step by step solution

Step 1:Given information

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Most popular questions from this chapter

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Find an equation of the line containing the point (−1,3,7)with direction vector (2,−4,9).(a) Use a different direction vector to find another equation for the same line. (b) Find an equation for the same line with the formx=at+5,y=bt+y0,z=ct+z0.

Short Answer

Step by step solution

Step 1:Given information

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Theoretical and Mathematical Physics

Statistics

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Find an equation of the line containing the point $(- 1, 3, 7)$ with direction vector $(2, - 4, 9)$ .
(a) Use a different direction vector to find another equation for the same line. (b) Find an equation for the same line with the form
$x = a t + 5, y = b t + y_{0}, z = c t + z_{0} .$