Questions about Chapter 3: Vectors.

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**

**Q1.
Vector A has a magnitude 6 cm and is at 36.9 ^{o} counterclockwise
from the + x-axis. It is added to a
vector B, and the resultant is a vector of magnitude 6 cm at 53.1^{o}
counterclockwise from the + y-axis.
Find the magnitude and direction of the vector
B.**

**ANS:
9.60 cm along the - x-axis.
**

**
Q2. Three displacement vectors are in
the same plane and are expressed as:
**

**ANS:
r = ( 7 i - 6 j ) m ; - 40.6 ^{o
}**

**Q3.
Two vectors are given by
**

** a
= 2 i + 3 j + 4 k and
b = i - 2 j + 3 k.
**

**Calculate
the vector c = 3 a - 2
b.
**

**ANS:
c = 4 i + 13 j + 6 k .
**

**Q4.
A car travels 30 km due south and then 40 km due west. Find the magnitude and
direction of the resultant displacement of the car.
Assume no change in the elevation
between the initial and final positions.
**

**ANS:
50 km ; 53.1 ^{o}
west of south.
**

**Q5.
Two vectors L and M are defined by
**

** L
= ( 4 i - 8 j ) m
and M = ( 8 i +
2 j ) m.
**

** Find
the magnitude and direction of the vector ( 2 L - M ).
**

**
ANS: 18.0 m at 270 ^{o}
with the + x-axis. = -18 j
**

**Q6.
Two points A and B are located in the xy-plane.
The Cartesian co-ordinates of A are (
1 , 4 ) and those of B are ( 4 , 1 ) , in m. Write, in unit vector notation, the
vector R that goes from point A to point
B. What is the distance between
points A and B ?
**

**ANS:
R = 3 i - 3 j
; Distance = 4.24 m.**

**Q****7****
Starting from airport A , an airplane flies 300 km east, then 400 km
northeast ( 45 ^{o} north of
east ), and then 100 km at an angle of 30^{o} west of north to arrive
finally at airport B.**

**(a)
What is the direct distance between airport A and airport B ?
**

**(b)
In what direction should a pilot of a direct flight from airport A to
airport B fly
the airplane ? ( Assume
there is no wind.)
**

**ANS:
648 km; 34.7 ^{o} N of E.
**

**Q****8****.
A person walks 12.0 km, 20 ^{o} south of east, and then walks 15.0
km, 10^{o} south of west.
Call these displacements A and B, respectively. **

**(a)
Write down in unit-vector notation these two displacements A and B. Take
east along the positive x-axis and
north along the positive y-axis.
**

**(b)
Find the magnitude and direction of the resultant vector.
**

**ANS: A = ( 11.3 i
- 4.10 j ) km ; B
= ( - 14.8 i - 2.61 j )
km
**

**ANS:
Magnitude = 7.57 km; Direction = 62.5 ^{o} S of W .
**

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