Homework – Lesson 1

1) Calculate e draw the vector w for the following cases

w = v

1

+ v

2

+

v

3

= 0i + 2j + 9k

w = v

1

+ v

2

-

v

3

w = v

1

- v

2

+

v

3

w = v

1

- v

2

–

v

3

with

v

1

= - 2i +2j + 3k

v

2

= 1i - 2j + 3k

v

3

= 1i +2j + 3k

2) Determine the x, y components of the following vectors

v = 2 v = 2 v = 5.5 v = 1 v = 2

0.5

v = 1.7i + 1j v = -1.7i + 1j

3) Determine and draw the unknown vectors in the following problems

Problem 1

v

1

+ v

2

+ v

3

= 0

v

1

is given, the directions of v

2

and v

3

are known

v

1

= 2i+1j

Problem 2

v

1

+ v

2

+ v

3

= 0

v

1

is given, the directions of v

2

and v

3

are known

v

1

= - 2i +2j

30

o

v

x

y

30

o

v

60

o

v

v

45

o

v

90

o

45

o

Line of application of v

2

Line of application of v

3

90

o

30

o

Line of application of v

2

Line of application of v

3

v

1

v

1

v

2

v

3

Solution:
v

2

= 1j ; v

3

= -2i -2j

Problem 3

v

1

+ v

2

= v

3

+ v

4

v

1

and v

2

are given, the directions of v

3

and v

4

are known

v

1

= - 2i + 2j

v

2

= - 2i – 2j

Problem 4

v

1

+ v

2

+ v

3

= v

4

v

1

and v

2

are given, the directions of v

3

and v

4

are known

v

1

= 1i + 2j

v

2

= - 3i

90

o

30

o

Line of application of v

3

Line of application of v

4

45

o

Line of application of v

4

Line of application of v

3

Solution:
v

3

= -2i -2j ; v

4

= -4i