Module 1: Part 2
Fundamental Concepts: Vectors
1.


Consider a vector A such that A  6 î  2 ĵ  k̂ . How would you write
the vector in a coordinate system where the unit vectors are û , v̂ , and
ŵ where
û 
2
1
1
î 
ĵ 
k̂
6
6
6
v̂ 
-1
1
1
î 
ĵ 
k̂
3
3
3
ŵ  0 î 
3
3
ĵ 
k̂
18
18

Hint: Write the vector in the form A  au û  av v̂  awŵ
Stop – Prepare To Outbrief
2.
For spherical coordinates,
A.
How would you write the position vector of a particle in spherical
coordinates? Draw a picture of your vector, coordinate system, and
unit vectors).
B.
Write the ρ̂ , ̂ , and θ̂ in terms of î , ˆj , and k̂ .
C.


The scalar product of two vectors A and B in Cartesian coordinates
is given by
 
A  B  A x B x  A y B y  A z Bz .
Is the scalar product in spherical coordinates
 
A  B  Aρ Bρ  A B  A B ?
θ θ
Explain your reasoning or provide a mathematical proof.
Stop – Prepare To Outbrief
3.
If the position vector of a particle is given by
 2
r  t  2t î  3 e 2t ĵ  2Sin(5t) k̂
A.
Find the initial velocity of the particle.
A.
Find the initial acceleration of the particle.


Stop – Prepare To Outbrief