IBV8 line L passes through the origin and is parallel to the vector 2i + 3j

In summary, the notation "IBV8 line" refers to a specific line labeled as "IBV8". A line passing through the origin means that the point (0,0) is on the line. To determine if a line is parallel to a vector, you can compare the slope of the line to the components of the vector. To graph a line that passes through the origin and is parallel to the vector 2i + 3j, you can plot the point (0,0) and a second point using the components of the vector. Yes, a line can be parallel to more than one vector as long as the slope is equal to the ratio of the components of the vectors.
  • #1
karush
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The line L passes through the origin and is parallel to the vector 2i + 3j.
Write down a vector equation for L.

\(\displaystyle r=(0,0)+s(2,3)\)

my question pending this is correct, could this be written as:

\(\displaystyle L=s(2,3)\):confused:
 
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  • #2
Yes, of course. I can't help but wonder why you are asking. I cannot imagine you being given a question like this without already know how to add vectors and multiply a vector by a number. s(2, 3)= (2s, 2s) and (0, 0)+ s(2, 3)= (0+ 2s, 0+ 3s)= (2s 3s).
 

FAQ: IBV8 line L passes through the origin and is parallel to the vector 2i + 3j

What does the notation "IBV8 line" refer to in this context?

The notation "IBV8 line" refers to a specific line that is named or labeled using that notation. It could represent any line, but in this case, it is referring to a line that has been labeled as "IBV8".

What does it mean for a line to pass through the origin?

A line passing through the origin means that the point (0,0) is on the line. In other words, the line intersects with the x and y axes at the point where they meet (0,0).

How do you determine if a line is parallel to a vector?

To determine if a line is parallel to a vector, you can compare the slope of the line to the components of the vector. If the slope of the line is equal to the ratio of the components of the vector, then the line is parallel to the vector.

How can you graph a line that passes through the origin and is parallel to the vector 2i + 3j?

To graph a line that passes through the origin and is parallel to the vector 2i + 3j, you can start by plotting the point (0,0) on the coordinate plane. Then, using the components of the vector, you can find a second point on the line. For example, if the vector is 2i + 3j, you can plot the point (2,3) on the line. Finally, connect the two points with a straight line to complete the graph.

Can a line be parallel to more than one vector?

Yes, a line can be parallel to more than one vector. As long as the slope of the line is equal to the ratio of the components of the vectors, it will be parallel to those vectors. In the case of the IBV8 line passing through the origin, it is parallel to all vectors with a ratio of 2:3 (e.g. 4i + 6j, 10i + 15j, etc.).

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