Direction vectors

[elleocin]

Find the vector equation of the line

a) that passes through the points A(2,0,-3) and B(-3,2,-2)

To find the direction vector d I subtracted B-A, which gives me (-3-2,2-0,-2+3) = (-5, 2, 1)

However, the answer in the textbook states that the direction vector is (5,-2-1) Why this is?
Is there a specific rule of changing the sign/factoring out negatives that I don't know about?

Any clarification would be much appreciated!:lol:

 

[pka]

Find the vector equation of the line
a) that passes through the points A(2,0,-3) and B(-3,2,-2)
To find the direction vector d I subtracted B-A, which gives me (-3-2,2-0,-2+3) = (-5, 2, 1)
However, the answer in the textbook states that the direction vector is (5,-2-1) Why this is?
Is there a specific rule of changing the sign/factoring out negatives that I don't know about?

If \(\displaystyle \vec{D}\) is the direction vector for a line \(\displaystyle \ell\) and \(\displaystyle \alpha\ne 0\) is a scalar then \(\displaystyle \alpha\vec{D}\) is also a direction vector for a line \(\displaystyle \ell\).

So \(\displaystyle -\vec{D}\) is.

 

[elleocin]

I'm sorry but I'm not quite sure what you mean by "[FONT=MathJax_Math]α[/FONT][FONT=MathJax_Main]≠[/FONT][FONT=MathJax_Main]0[/FONT]is a scalar then [FONT=MathJax_Math]α[/FONT][FONT=MathJax_Math]D[/FONT] is also a direction vector for a line [FONT=MathJax_Main]ℓ[/FONT]."

What exactly is "[FONT=MathJax_Math]α[/FONT][FONT=MathJax_Math]D"? and what value does "a" stand for? [/FONT]

 

[pka]

I'm sorry but I'm not quite sure what you mean by "[FONT=MathJax_Math]α[/FONT][FONT=MathJax_Main]≠[/FONT][FONT=MathJax_Main]0[/FONT]is a scalar then [FONT=MathJax_Math]α[/FONT][FONT=MathJax_Math]D[/FONT] is also a direction vector for a line [FONT=MathJax_Main]ℓ[/FONT]."
What exactly is "[FONT=MathJax_Math]α[/FONT][FONT=MathJax_Math]D"? and what value does "a" stand for? [/FONT]

Why are you doing vectors if you have no idea about the vocabulary of vectors.
Do you know what a non-zero scalar is?
Do you know how to multiply a scalar times a vector?

 

[DrPhil]

Find the vector equation of the line

a) that passes through the points A(2,0,-3) and B(-3,2,-2)

To find the direction vector d I subtracted B-A, which gives me (-3,2,-2)-(2,0,-3) = (-5, 2, 1)

However, the answer in the textbook states that the direction vector is (5,-2-1) Why this is?
Is there a specific rule of changing the sign/factoring out negatives that I don't know about?

Any clarification would be much appreciated!:lol:

You chose the direction from A to B, which is the same I would have done. As pka has pointed out, you can multiply a vector by any non-zero constant and it will still represent the same direction.

 

[pka]

As pka has pointed out, you can multiply a vector by any non-zero constant and it will still represent the same direction.

One minor correction if the scalar is positive the direction is the same.
Of the scalar is negative the direction is opposite.