Vectors

Find the scalar product of the vectors and .

bakjia 3 kib 6

Which of the following is equal to?

2r

r r1.

rr 2.

2)( rr 3.

None of these4.

Find the value of if the vectors and

are perpendicular.

FkFjia 63 kjiFb 32

F

Find the angle between the vectors and .kia 3 kjib 32

If , what is the magnitude of ?

kjia 23 a

Two forces act upon an object. The first has magnitude 3 N in an easterly direction and the second has magnitude 4 N in a southerly direction. What is the direction of the resultant force?

is the point (4,-2). Find . OP��������������

P

is the point (3,2,-6). Find .P OP��������������

What is the length of the vector ?kjia 23

21.

142.

63.

24.

If two vectors are perpendicular then .0ba

1. True

2. False

3. Don’t know

Does ?abba

1. Yes

2. No

Find if and .

bakjib 32 kjia 36

Enter the second component of if and .

bakjia 3 kib 2

Find the area of a triangle with vertices at , and . 1,2,5 2,3,1 1,2,3

What is the value of x?

θ

1. x= y cosθ

2. x= z sinθ

3. x= y sinθ

4. x= z cosθ

A javelin is released with initial velocity Vo=13 m/s at an angle of 38° to the

horizontal. What is the vertical component of the initial velocity?

If and ,what is ?

jip 6 jiq 3qp

ji 47 1.

112.

93.

ji 27 4.

Which vectors must always start at the origin?

1. Unit vectors

2. Position vectors

3. Column vectors

4. None of these

What is the position vector of the point with coordinates ? 4,2

ji 42 1.

ji 42 2.

ji 42 3.

ji 42 4.

is the point (3,-1). Find the unit vector in the direction .

QOQ��������������

10

21.

ji 10

22.

ji10

1

10

3

3.

10

1

10

3

4.

What is meant by the symbol ?j

1. It is the unit vector in the positive x-direction

2. It is the unit vector in the positive y-direction

3. It is a vector in the positive x-direction

4. It is a vector in the positive y-direction

Consider the point P(3,2). What is the direction ratio of the vector ?OP

P and Q have coordinates (-5,-1) and (1,2) respectively. Find the

direction cosines of .PQ

45

3,

45

6 1.

45

3,

45

62.

45

3,

45

6 3.

45

3,

45

64.

Find for the two points and . 2,7A 1,2BAB

ji 91.

ji 92.

ji 35 3.

ji 35 4.