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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 9.1, Problem 37E
Textbook Problem
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Magnitude of Vectors Find | u |, | v |, | 2u |, | 1 2 v | , | u + v |, | uv |, and | u | − | v |.

37. u = 2i + j, v = 3i − 2j

To determine

To find: Values of |u| , |v| , |2u| , |12v| , |u+v| , |uv| and |u||v| .

Explanation of Solution

Formula used:

The vector u=a1,a2 can be expressed in terms of i and j as u=a1,a2=a1i+a2j (1)

The magnitude of a vector u=a1,a2 is |u|=a12+a22 (2)

Where, a1 is horizontal component of vector v and a2 is vertical component of vector v.

If u is a vector, then |cu|=|c||u| (3)

Where cR .

If vector u=a1,a2 and v=b1,b2 then,

u+v=a1+b1,a2+b2 (4)

uv=a1b1,a2b2 (5)

Calculation:

Section (1):

Vector u is given as u=2i+j .

Use equation (1) to express vector u into component form.

u=2i+j=2,1

Substitute 2 for a1 and 1 for a2 in equation (2),

|u|=22+12=4+1=5

Thus, value of |u| is 5 .

Section (2):

Vector v is given as v=3i2j .

Use equation (1) to express vector v into component form.

v=3i2j=3,2

Substitute 3 for a1 and 2 for a2 in equation (2), to get the magnitude.

|v|=32+(2)2=9+4=13

Thus, value of |v| is 13 .

Section (3):

Vector u is u=2i+j .

From Section (1), value of |u| is 5 .

Substitute 2 for c and 5 for |u| in equation (3),

|2u|=2×|u|=25

Thus, value of |2u| is 25_ .

Section (4):

Vector v is given as v=3i2j .

From section (2), value of |v| is 13 .

Substitute 12 for c and 13 for |v| in equation (3).

|12v|=12×|v|=12×13=132

Thus, value of |12v| is 132 .

Section (5):

Vector u is u=2i+j and vector v is v=3i2j

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Chapter 9 Solutions

Precalculus: Mathematics for Calculus (Standalone Book)
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Ch. 9.1 - Component Form of Vectors Express the vector with...Ch. 9.1 - Component Form of Vectors Express the vector with...Ch. 9.1 - Component Form of Vectors Express the vector with...Ch. 9.1 - Component Form of Vectors Express the vector with...Ch. 9.1 - Component Form of Vectors Express the vector with...Ch. 9.1 - Component Form of Vectors Express the vector with...Ch. 9.1 - Component Form of Vectors Express the vector with...Ch. 9.1 - Component Form of Vectors Express the vector with...Ch. 9.1 - Sketching Vectors Sketch the given vector with...Ch. 9.1 - Sketching Vectors Sketch the given vector with...Ch. 9.1 - Sketching Vectors Sketch the given vector with...Ch. 9.1 - Sketching Vectors Sketch the given vector with...Ch. 9.1 - Sketching Vectors Sketch representations of the...Ch. 9.1 - Sketching Vectors Sketch representations of the...Ch. 9.1 - Sketching Vectors Sketch representations of the...Ch. 9.1 - Sketching Vectors Sketch representations of the...Ch. 9.1 - Writing Vectors in Terms of i and j Write the...Ch. 9.1 - Writing Vectors in Terms of i and j Write the...Ch. 9.1 - Writing Vectors in Terms of i and j Write the...Ch. 9.1 - Writing Vectors in Terms of i and j Write the...Ch. 9.1 - Operations with Vectors Find 2u, 3v, u + v, and 3u...Ch. 9.1 - Operations with Vectors Find 2u, 3v, u + v, and 3u...Ch. 9.1 - Operations with Vectors Find 2u, 3v, u + v, and 3u...Ch. 9.1 - Operations with Vectors Find 2u, 3v, u + v, and 3u...Ch. 9.1 - Operations with Vectors Find 2u, 3v, u + v, and 3u...Ch. 9.1 - Operations with Vectors Find 2u, 3v, u + v, and 3u...Ch. 9.1 - Magnitude of Vectors Find | u |, | v |, | 2u |,...Ch. 9.1 - Magnitude of Vectors Find | u |, | v |, | 2u |,...Ch. 9.1 - Magnitude of Vectors Find | u |, | v |, | 2u |,...Ch. 9.1 - Magnitude of Vectors Find | u |, | v |, | 2u |,...Ch. 9.1 - Components of a Vector Find the horizontal and...Ch. 9.1 - Components of a Vector Find the horizontal and...Ch. 9.1 - Components of a Vector Find the horizontal and...Ch. 9.1 - Components of a Vector Find the horizontal and...Ch. 9.1 - Components of a Vector Find the horizontal and...Ch. 9.1 - Components of a Vector Find the horizontal and...Ch. 9.1 - Magnitude and Direction of a Vector Find the...Ch. 9.1 - Magnitude and Direction of a Vector Find the...Ch. 9.1 - Magnitude and Direction of a Vector Find the...Ch. 9.1 - Magnitude and Direction of a Vector Find the...Ch. 9.1 - Magnitude and Direction of a Vector Find the...Ch. 9.1 - Magnitude and Direction of a Vector Find the...Ch. 9.1 - Components of a Force A man pushes a lawn mower...Ch. 9.1 - Components of a Velocity A jet is flying in a...Ch. 9.1 - Velocity A river flows due south at 3 mi/h. 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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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