If you have 2i + j would the point be ( 2,1) or 2,0? So what is j equal to in vectors when it is not with another number?
2 i + j = 2 i + 1 j
is a vector of length 2 in the x direction and length 1 in the y direction
i is the unit vector in the x direction
j is the unit vector in the y direction.
Note there are no "points" involved, only lengths.
A vector from the origin to (2,1) would be 2-0 in the x direction and 1 - 0 in the y direction so would be 2 i + j
HOWEVER a vector from (3,3) to (5,4) would also be 2 i + j
as would (17, 18) to (19,19)
vectors have directions and sizes, they do not have "points". You can go east 2 and north 1 from anywhere.
Okay that makes sense, I wasn't sure what value the j had when it was by itself, to find magnitude.It makes sense that it is 1 and is the length in the y direction.Thanks!
You are welcome.
To determine the value of j in the vector expression 2i + j, we need more information. Vectors are typically represented as quantities that have both magnitude and direction. In this case, we have the vector expression 2i + j, where i and j are unit vectors in the x and y directions, respectively.
If you are referring to Cartesian coordinates, we can interpret the vector expression 2i + j as a displacement in the x-direction and y-direction. The coefficient 2 in front of i means that the displacement in the x-direction is twice the unit displacement, while j alone indicates one unit of displacement in the y-direction.
In this context, the vector 2i + j would correspond to the point (2, 1). The 2i component accounts for the displacement in the x-direction, which would be 2 units, and the j component accounts for the displacement in the y-direction, which would be 1 unit.
If you are referring to another coordinate system or a different context, please provide more information so I can assist you better.