Answer:
draw a line that goes up to 8 from the origin.
Step-by-step explanation:
The sum of the vector 2u and vector 4v is 2i+12j and it can be drawn with the coordinates point (2, 12) on the coordinate plane.
It is defined as a physical quantity that has magnitude as well as direction. Vector always follows a triangle rule for the sum of the two vectors.
We have given two vectors shown in the coordinate plane that is:
u(-1, 2) and v(1, 2)
We can write these two vectors in the form of i and j
[tex]\rm \vec{u}= -\hat{i}+2\hat{j}\\\rm \vec{v}= \hat{i}+2\hat{j}[/tex]
Finding vector 2u:
[tex]\rm \vec{2u}= -2\hat{i}+4\hat{j}\\[/tex] (multiply by scalar value 2 in the vector u)
Finding vector 4v:
[tex]\rm \vec{4v}= 4\hat{i}+8\hat{j}[/tex] (multiply by scalar value 4 in the vector v)
Now find the sum of the vector 2u and vector 4v:
[tex]\rm \vec{2u}+ \vec{4v}= -2\hat{i}+4\hat{j}+4\hat{i}+8\hat{j}[/tex]
[tex]\rm \vec{2u}+ \vec{4v}= 2\hat{i}+12\hat{i}[/tex]
Now representing the vector (2u+4v) on the coordinate plane with coordinates (2, 12) as shown in the picture.
Thus, the sum of the vector 2u and vector 4v is 2i+12j and it can be drawn with the coordinates point (2, 12) on the coordinate plane.
Learn more about the vector here:
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