Why the order of the cross product matter?

You are, again, combining unlike terms. You should have learned not to do this long before you cover this topic.

It is not true that -7 + -7t = -14t. All the others have the same error.

If t = 1, then -7 + -7t = -14t; but, for example, if t = 2, then -7 + -7t = -7 + -14 = -21, while -14t = -28. These are not equal.

If you plug the first form of each expression (e.g. x = -7 + -7t) into the equations, everything works (for both solutions).

In fact, your x = 0t, y = 0t, z = 1t does not satisfy the equations (for all t). You seem to be ignoring the fact that t is a variable everywhere!
 
Dr.Peterson said:
You are, again, combining unlike terms. You should have learned not to do this long before you cover this topic.

It is not true that -7 + -7t = -14t. All the others have the same error.

If t = 1, then -7 + -7t = -14t; but, for example, if t = 2, then -7 + -7t = -7 + -14 = -21, while -14t = -28. These are not equal.

If you plug the first form of each expression (e.g. x = -7 + -7t) into the equations, everything works (for both solutions).

In fact, your x = 0t, y = 0t, z = 1t does not satisfy the equations (for all t). You seem to be ignoring the fact that t is a variable everywhere!
Click to expand...
I know I can't combine unlike terms, I was just following a tutorial on youtube and I thought it was a dirty shortcut for these problems. Thank you, for your help, by the way, can I just leave the expression in their first form, and say that's the answer?
for example:
x= -7 + 7t
y= 4 - 4t
z= 1t
 
[QUOTE="Gavriell, post: 458930, member: 71605"[/QUOTE]
This is the sort of question that simply dives me crazy.
\(\displaystyle \vec{u}\times\vec{v}=-\vec{v}\times\vec{u}\) If it is that simple what is the big deal?
Lets teach the basic concepts. If \(\displaystyle \vec{u}\) is that direction vector of a line or a normal vector of a plane than so is \(\displaystyle -\vec{u}\) have that property for the same line or plane.
 
Gavriell said:
I know I can't combine unlike terms, I was just following a tutorial on youtube and I thought it was a dirty shortcut for these problems. Thank you, for your help, by the way, can I just leave the expression in their first form, and say that's the answer?
for example:
x= -7 + 7t
y= 4 - 4t
z= 1t
Click to expand...
I imagine they must have been doing something different on the tutorial that just looked like they were combining those terms. If you don't know why a shortcut someone else takes is legal, don't follow -- you might get into real trouble! Do what you know is right.

Yes, of course you can (should!) leave the equations in those forms -- unless you choose to write the last one as z = t, as I would, or to write x = 7t - 7. That's a matter of taste.
 
Dr.Peterson said:
I imagine they must have been doing something different on the tutorial that just looked like they were combining those terms. If you don't know why a shortcut someone else takes is legal, don't follow -- you might get into real trouble! Do what you know is right.

Yes, of course you can (should!) leave the equations in those forms -- unless you choose to write the last one as z = t, as I would, or to write x = 7t - 7. That's a matter of taste.
Click to expand...
ok Thank you!
 
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