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Vectors in Plane - Calculus - Exercise, Exercises of Calculus

National Institute of Industrial EngineeringCalculus

This file contains some problems related calculus. Some hints to the given problems are: Vectors in Plane, Component, Magnitude, Indicated Vector, Magnitude of the Vector, Unit Vector, Given Vector, Indicated Form, Component Form, Direction

Typology: Exercises

2011/2012

Uploaded on 12/31/2012

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Vectors in Plane
Findthecomponentformandmagnitudeoftheindicatedvector.
1) GiventhatP=(5,8)andQ=(6,9),findthecomponentformandmagnitudeofthevectorPQ .
A) 1
,
1
,
2B)1,1 ,2 C) -1
,
-1
,
2D)
-1,-1 ,2
2) GiventhatP=(-1,6)andQ=(0,1),findthecomponentformandmagnitudeofthevectorPQ.
A) -1,-5, 26 B) 1
,
-5
,
26 C) -1,5 ,26 D) 1,-5 ,26
3) GiventhatP=(11,5)andQ=(3,10),findthecomponentformandmagnitudeofthevectorQP .
A) 8,-5,89 B) -8
,
5
,
89 C) 8
,
-5
,
89 D) -8,5 ,89
4) GiventhatP=(-8,-6)andQ=(-7,3),findthecomponentformandmagnitudeofthevector5QP.
A) 1 5,95,410 B) -15,-95,582
C) -15,-95,410 D) -9,-45 ,582
5) GiventhatP=(6
,
-5),Q=(4
,
-6),R=(-5
,
-1),andS=(-9
,
-8),findthecomponentformandmagnitudeofthe
vectorPQ +3RS.
A) -6
,
-8
,
10 B) 14,22 ,2 170 C) -14,-22 ,2 170 D) -14
,
-22
,
680
Findthecomponentformoftheindicatedvector.
6) Letu=-3
,
4
,
v=8
,
2 .Findu+v.
A) -11
,
2 B) 1
,
10 C) -1
,
12 D) 5
,
6
7) Letu=-3
,
-2
,
v=1
,
-5 .Findu-v.
A) 2
,
-3 B) -4
,
3 C) -2
,
-7 D) -1
,
6
8) Letu=-2
,
7
,
v=-6
,
-5 .Findv-u.
A) -3
,
-13 B) -8
,
2 C) -4
,
-12 D) 9
,
1
9) Letu=-6
,
7 .Find6u.
A) 36
,
42 B) -36
,
42 C) -36
,
-42 D) 36
,
-42
10) Letu=3
,
-1
,
v=-6
,
-6 .Find9u+2v.
A) 18
,
-24 B) -27
,
-14 C) 15
,
-21 D) 39
,
3
11) Letu=-5
,
2
,
v=-2
,
6 .Find4u+3v.
A) -26
,
8 B) -14
,
-10 C) -28
,
32 D) -26
,
26
Findtheunitvectorinthedirectionofthegivenvector.Writeyouranswerintheindicatedform.
12) Letu=2
,
1 .Findtheunitvectorinthedirectionofu
,
andwriteyouranswerincomponentform.
A) 2
3,1
3B) 2
5,1
5C) 2
5,1
5D) 1,1
pf3

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Vectors in Plane

Find the component form and magnitude of the indicated vector.

  1. Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of the vector PQ. A) 1, 1 , 2 B) 1, 1 , 2 C) - 1, - 1 , 2 D) - 1, - 1 , 2

  2. Given that P = (-1, 6) and Q = (0, 1), find the component form and magnitude of the vector PQ. A) - 1, - 5 , 26 B) 1, - 5 , 26 C) - 1, 5 , 26 D) 1, - 5 , 26

  3. Given that P = (11, 5) and Q = (3, 10), find the component form and magnitude of the vector QP. A) 8, - 5 , 89 B) - 8, 5 , 89 C) 8, - 5 , 89 D) - 8, 5 , 89

  4. Given that P = (-8, - 6) and Q = (-7, 3), find the component form and magnitude of the vector 5 QP. A) 1 5, 9 5 , 410 B) - 1 5, - 9 5 , 5 82 C) - 1 5, - 9 5 , 410 D) - 9, - 45 , 5 82

  5. Given that P = (6, - 5), Q = (4, - 6), R = (-5, - 1), and S = (-9, - 8), find the component form and magnitude of the vector PQ + 3 RS. A) - 6, - 8 , 10 B) 14, 22 , 2 170 C) - 14, - 22 , 2 170 D) - 14, - 22 , 680

Find the component form of the indicated vector.

  1. Let u = - 3, 4 , v = 8, 2. Find u + v. A) - 11, 2 B) 1, 10 C) - 1, 12 D) 5, 6

  2. Let u = - 3, - 2 , v = 1, - 5. Find u - v. A) 2, - 3 B) - 4, 3 C) - 2, - 7 D) - 1, 6

  3. Let u = - 2, 7 , v = - 6, - 5. Find v - u. A) - 3, - 13 B) - 8, 2 C) - 4, - 12 D) 9, 1

  4. Let u = - 6, 7. Find 6 u. A) 36, 42 B) - 36, 42 C) - 36, - 42 D) 36, - 42

  5. Let u = 3, - 1 , v = - 6, - 6. Find 9 u + 2 v. A) 18, - 24 B) - 27, - 14 C) 15, - 21 D) 39, 3

  6. Let u = - 5, 2 , v = - 2, 6. Find 4 u + 3 v. A) - 26, 8 B) - 14, - 10 C) - 28, 32 D) - 26, 26

Find the unit vector in the direction of the given vector. Write your answer in the indicated form.

  1. Let u = 2, 1. Find the unit vector in the direction of u , and write your answer in component form. A) 23 , 13 B) 2 5

C) 25 , 15 D) 1, 1

PreCalculus

  1. Let u = 1, 3. Find the unit vector in the direction of u , and write your answer as a linear combination of the standard unit vectors i and j. A) 1 10

i + 3 10

j B) 101 i + 103 j C) i + j D)^14 i + 34 j

  1. Let u = - 2, - 3. Find the unit vector in the direction of u , and write your answer as a linear combination of the standard unit vectors i and j. A) -^2 13

i + -^3 13

j B) i + j C) -^2 5

i + -^3 5

j D) -^2 13

i + -^3 13

j

  1. Let u = 4, - 3. Find the unit vector in the direction of u , and write your answer as a linear combination of the standard unit vectors i and j. A)^4 7

i - 3 7

j B) 4 25

i - 3 25

j C) 1, 1 D)^4 5

i - 3 5

j

  1. Let u = - 2 i - 3 j. Find the unit vector in the direction of u , and write your answer as a linear combination of the standard unit vectors i and j. A) -^2 13

i + 3 13

j B) -^2 13

i - 3 13

j C) - 2 13

i - 3 13

j D) - 2 5

i - 3 5

j

Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0 ° , 360 ° ) rounded to the nearest tenth.

  1. 1, 6 A) 37, 189.5° B) 37, 260.5° C) 37, 9.5° D) 37, 80.5°

A) 26, 78.7° B) 26, 11.3° C) 26, 101.3° D) 26, 168.7°

A) 82, 96.3° B) 82, 173.7° C) 82, 353.7° D) 82, 276.3°

A) 221, 109.7° B) 221, 250.3° C) 221, 160.3° D) 221, 199.7°

A) 8, 180° B) 8, 0° C) - 8, 0° D) - 8, 180°

    • 2 i + 5 j A) 7, 291.8° B) 29, 111.8° C) 29, 68.2° D) 29, 111.8°

  2. 10(cos 217° i + sin 217° j ) A) 10, 217° B) 10, 37° C) 10, 217° D) 100, 37°

Calin M. Agut - 2012