Find the vector-equation of line that goes through the point P in the direction of u?

[blazekid43]

[h=1]I dont know what forumla I would need to do an equation like this one.


Find the vector-equation of line that goes through the point P_0 in the direction[/h]of u:

i. P₀ (1, 2, 3) and u = <1,-1,2>
ii. P₀ (1, 1, 0) and u = <1,1,0>

Help would be appreciated

 

[DrPhil]

I dont know what forumla I would need to do an equation like this one.


Find the vector-equation of line that goes through the point P_0 in the direction

of u:

i. P₀ (1, 2, 3) and u = <1,-1,2>
ii. P₀ (1, 1, 0) and u = <1,1,0>

Help would be appreciated

Think of the line as a straight-line trajectory, written parametrically as a function of \(\displaystyle t\).
Each component is equal to the starting value plus \(\displaystyle t\) times the corresponding element of velocity vector \(\displaystyle u\).

\(\displaystyle P = P_0 + \vec{u} \times t\)

 

[blazekid43]

Think of the line as a straight-line trajectory, written parametrically as a function of \(\displaystyle t\).

Each component is equal to the starting value plus \(\displaystyle t\) times the corresponding element of velocity vector \(\displaystyle u\).

\(\displaystyle P = P_0 + \vec{u} \times t\)

Hmmm, Okay I sort of get it but what does "t" equal to? I kept reading what you said over and over and I can understand everything but the "t"?

I'm just guessing here but, would this be right?

i) < 1+1t, 2-1t, 3+2t>
ii) < 1+t, 1+t, 0>

 

[HallsofIvy]

Would you have preferred it if Dr. Phil had said "\(\displaystyle P_0+ ux\)" rather than "\(\displaystyle P_0+ ut\)"? Do you not know what a "variable" is? A line has an infinite number of points. Each individual value of the variable, whether it is called "t" or "x" or any other name, identifies one of those points. When t= 0, \(\displaystyle P_0+ tu= P_0\) which, here, is (1, 2, 3), the first point. When t= 1, \(\displaystyle P_0+ tu= P_0+ u= (1, 2, 3)+ (1, -1, 2)= (2, 1, 5), \)etc.

 

[blazekid43]

Would you have preferred it if Dr. Phil had said "\(\displaystyle P_0+ ux\)" rather than "\(\displaystyle P_0+ ut\)"? Do you not know what a "variable" is? A line has an infinite number of points. Each individual value of the variable, whether it is called "t" or "x" or any other name, identifies one of those points. When t= 0, \(\displaystyle P_0+ tu= P_0\) which, here, is (1, 2, 3), the first point. When t= 1, \(\displaystyle P_0+ tu= P_0+ u= (1, 2, 3)+ (1, -1, 2)= (2, 1, 5), etc.\)

\(\displaystyle

Lol yeah, I do know what a variable is.
In my last post where I tried to get the equation

i) < 1+1t, 2-1t, 3+2t>
ii) < 1+t, 1+t, 0>

I assumed t was a variable.

As my original question was

Find the vector-equation of line that goes through the point P_0 in the direction of u:

I need to confirm whether that what I have done is right.\)

 

[Deleted member 4993]

Lol yeah, I do know what a variable is.
In my last post where I tried to get the equation

I assumed t was a variable.

As my original question was
I need to confirm whether that what I have done is right.

Does unit the vector (of the resultant vector) match-up with the unit vector of "u"?

Does the resultant vector go through the given point?

If the answer to both the questions is YES - then most probably the answer is correct.

You can check your own answer!