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Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
Publisher: Brooks Cole
ISBN: 9781305071759

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BuyFindarrow_forward

Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
Publisher: Brooks Cole
ISBN: 9781305071759
Chapter 9.2, Problem 32E
Textbook Problem
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Vector Projection of u onto v (a) Calculate projv u. (b) Resolve u into u1 and u2, where u1 is parallel to v and u2 is orthogonal to v.

32. u = 〈11, 3〉, v = 〈−3, −2〉

(a)

To determine

To find: The projection of u onto v.

Explanation of Solution

Given:

The given vector u is 11,3 and vector v is 3,2 .

Formula used:

The projection of u onto v is,

projvu=(uv|v|2)v (1)

Calculation:

The formula to calculate dot product of two vectors u=a1i+a2j and v=b1i+b2j is,

uv=a1b1+a2b2

Substitute 11 for a1 , 3 for b1 , 3 for a2 and 2 for b2 in the above formula.

uv=(11)(3)+(3)(2)=336=39

(b)

To determine

To find: Resolved form of vector u into u1 and u2 .

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Chapter 9 Solutions

Precalculus: Mathematics for Calculus (Standalone Book)
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(a) Find u 3v....Ch. 9 - Let u=43,4. (a) Graph u in the coordinate plane,...Ch. 9 - A river is flowing due east at 8 mi/h. A man heads...Ch. 9 - Let u = 3i + 2j and v = 5i j. (a) Find the angle...Ch. 9 - Find the work done by the force F = 3i 5j in...Ch. 9 - Let P(4, 3, 1) and Q(6, 1, 3) be two points in...Ch. 9 - Calculate the given quantity if u = i + j 2k v =...Ch. 9 - Find two unit vectors that are perpendicular to...Ch. 9 - (a) Find a vector perpendicular to the plane that...Ch. 9 - Find parametric equations for the line that...Ch. 9 - Sketch the vector field F by drawing a diagram as...Ch. 9 - Sketch the vector field F by drawing a diagram as...Ch. 9 - Sketch the vector field F by drawing a diagram as...Ch. 9 - Sketch the vector field F by drawing a diagram as...Ch. 9 - Sketch the vector field F by drawing a diagram as...Ch. 9 - Sketch the vector field F by drawing a diagram as...Ch. 9 - Sketch the vector field F by drawing a diagram as...Ch. 9 - Sketch the vector field F by drawing a diagram as...Ch. 9 - Sketch the vector field F by drawing a diagram as...Ch. 9 - Sketch the vector field F by drawing a diagram as...Ch. 9 - Match the vector field F with the graphs labeled...Ch. 9 - Match the vector field F with the graphs labeled...Ch. 9 - Match the vector field F with the graphs labeled...Ch. 9 - Match the vector field F with the graphs labeled...Ch. 9 - Match the vector field F with the graphs labeled...Ch. 9 - Match the vector field F with the graphs labeled...Ch. 9 - Match the vector field F with the graphs labeled...Ch. 9 - Match the vector field F with the graphs labeled...Ch. 9 - Flow Lines in a Current The current in a turbulent...

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