Component Form of Vector v...2

[nycmathguy]

Section 6.3

Can you please 70? What does mean that v is in the direction of I + 3j?

 

[MathLover1]

correct

I suggest you to use simple way to do it:

Express the following vector in component form:

v=<x,y>

x=||v||cos(delta)
y=||v|sin(delta)

 

[MathLover1]

70.
||v||=2->Magnitude of the vector
v in direction i+ 3j
The standard form of the vector is image v=ai+bj, so a=1 and b=3

Direction angle is tan(θ )=a/b=1/3
θ =tan^-1(1/3)
θ = 18.43°

Express the following vector in component form:

v=<x,y>

x=2cos(18.43°)=1.89742
y=2sin(18.43°)=0.63229

v=<1.89742,0.63229>

 

[nycmathguy]

70.
||v||=2->Magnitude of the vector
v in direction i+ 3j
The standard form of the vector is image v=ai+bj, so a=1 and b=3

Direction angle is tan(θ )=a/b=1/3
θ =tan^-1(1/3)
θ = 18.43°

Express the following vector in component form:

v=<x,y>

x=2cos(18.43°)=1.89742
y=2sin(18.43°)=0.63229

v=<1.89742,0.63229>

Thank you. What does mean that v is in the direction of I + 3j?

 

[MathLover1]

means vector v is in the direction of vector i + 3j (standard form of the vector ai+bj)
its direction is given by v/||v||

 

[nycmathguy]

means vector v is in the direction of vector i + 3j (standard form of the vector ai+bj)
its direction is given by v/||v||

Why are vectors needed to do most of Calculus 3?

 

[MathLover1]

Vectors are useful tools for solving two-dimensional problems. Life, however, happens in three dimensions. To expand the use of vectors to more realistic applications, it is necessary to create a framework for describing three-dimensional space.

 

[nycmathguy]

Vectors are useful tools for solving two-dimensional problems. Life, however, happens in three dimensions. To expand the use of vectors to more realistic applications, it is necessary to create a framework for describing three-dimensional space.

Are you talking about vector functions?

 

[MathLover1]

yes,
def.: A vector function is a function that takes one or more variables and returns a vector.

 

[nycmathguy]

yes,
def.: A vector function is a function that takes one or more variables and returns a vector.

Thanks. We can worry about vector functions if and when I get to calculus 3. Interesting idea this vector function taking one or more variables and spitting out a vector.