Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 9, Problem 24SP
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4. a. If 37– 2ỷ = đ and 53 – 3ỷ = b, express the vectors i and y in terms of
a and b.
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b. Solve for a, b, and c: (2, –1, c) + (a, b, 1) – 3(2, a, 4) = (-3, 1, 2c).
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1. The distance of a point in the 3-D system from the origin
a. is defined by the absolute value of the vector from the origin to this point.
b. is the square root of the square of the sums of the x-, y- and z-values.
c. is the square root of the sum of the squares of x-, y- and z-values.
d. can either be negative or positive.
e. None of the above.
2. In parametrizing lines connected by two points in 3-D plane,
a. there is only one correct parametrization.
b. symmetry equations may not exist.
c. a, b, and c must not be equal to 0.
d. the vector that connects the two points is a scalar multiple of the vector containing the direction numbers.
e. None of the above.
3. A plane in 3D-space system
a. is generated by at least three points.
b. can lie in more than one octant.
c. must have a z-dimension.
d. must have a point other than the origin.
e. None of the above.
4. A quadric surface
a. must have either x2, y2, or z2 or a combination of those, on its general expression.
b. must have a…
14. Given that a and bare two vectors, then the
vector (a + b) x (a – b) is
A. perpendicular to (a – b)
B. parallel to (a – b)
C. parallel to (a + b)
D. equal to (2a – b)
Chapter 9 Solutions
Calculus
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Prob. 58PSCh. 9.7 - Prob. 59PSCh. 9.7 - Prob. 60PSCh. 9 - Prob. 1PECh. 9 - Prob. 2PECh. 9 - Prob. 3PECh. 9 - Prob. 4PECh. 9 - Prob. 5PECh. 9 - Prob. 6PECh. 9 - Prob. 7PECh. 9 - Prob. 8PECh. 9 - Prob. 9PECh. 9 - Prob. 10PECh. 9 - Prob. 11PECh. 9 - Prob. 12PECh. 9 - Prob. 13PECh. 9 - Prob. 14PECh. 9 - Prob. 15PECh. 9 - Prob. 16PECh. 9 - Prob. 17PECh. 9 - Prob. 18PECh. 9 - Prob. 19PECh. 9 - Prob. 20PECh. 9 - Prob. 21PECh. 9 - Prob. 22PECh. 9 - Prob. 23PECh. 9 - Prob. 24PECh. 9 - Prob. 25PECh. 9 - Prob. 26PECh. 9 - Prob. 27PECh. 9 - Prob. 28PECh. 9 - Prob. 29PECh. 9 - Prob. 30PECh. 9 - Prob. 1SPCh. 9 - Prob. 2SPCh. 9 - Prob. 3SPCh. 9 - Prob. 4SPCh. 9 - Prob. 5SPCh. 9 - Prob. 6SPCh. 9 - Prob. 7SPCh. 9 - Prob. 8SPCh. 9 - Prob. 9SPCh. 9 - Prob. 10SPCh. 9 - Prob. 11SPCh. 9 - Prob. 12SPCh. 9 - Prob. 13SPCh. 9 - Prob. 14SPCh. 9 - Prob. 15SPCh. 9 - Prob. 16SPCh. 9 - Prob. 17SPCh. 9 - Prob. 18SPCh. 9 - Prob. 19SPCh. 9 - Prob. 20SPCh. 9 - Prob. 21SPCh. 9 - Prob. 22SPCh. 9 - Prob. 23SPCh. 9 - Prob. 24SPCh. 9 - 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- 2. If , and the vector is drawn with its tail at the point, find the coordinates of the point at the head of .arrow_forwardTake this test to review the material in Chapters 4and Chapters 5. After you are finished, check your work against the answers in the back of the book. Write w=(7,2,4) as a linear combination of the vectors v1, v2 and v3 if possible. v1=(2,1,0), v2=(1,1,0), v3=(0,0,6)arrow_forwardWe mentioned in Section 7.5 that our algebraic treatment of vectors could be attributed, in part, to the Irish mathematician William Rowan Hamilton. Hamilton considered his greatest achievement to be the discovery of qualernions, which he (incorrectly) predicted would revolutionize physics. Research the subject of quaternions. What are they? Why did quaternions fail to be as useful for physics as Hamilton predicted? How are quaternions useful, instead, for 3.D computer graphics? Write a paragraph or two about your findings.arrow_forward
- Solve 25 & 27 Please and thank you.arrow_forward3. If a = 3x - 5ỹ and b = -2x +9y, write the vector 5a-86 in terms of x and yarrow_forward6. Explain in words how a student would determine the magnitude of the vector P[2, 3, 1]. There is no need to solve the problem. You will be marked on how well you communicate your ideas. (arrow_forward
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- 4. For which value of k the vector u = is a linear combination of the vectors k 3 2 3 V1 = and v2 = -1 of the vectors vị = and v2 =arrow_forward2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 = 3 + 2x + 5x². pi i. -9-7x - 15x² ii. 6+11x + 6x² = iii. O iv. 7 + 8x + 9x² b. Suppose that vi = = (2, 1, 0, 3), v₂ = (3, −1, 5, 2), and №3 = (–1, 0, 2, 1). Which of the following vectors are in span {1, 2, 3}? i. (2, 3, -7,3) ii. (0,0,0,0) iii. (1,1,1,1) iv. (-4, 6, -13, 4)arrow_forwardProblem 6. Suppose that V₁, V2 and v3 are linearly independent vectors in a vector space V. Prove that the vectors W₁ = V₁ + V2, W2 = V₂ + V3 and w3 = V3 + V₁ are also linearly independent in V.arrow_forward
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