Question

select all that apply
when adding vectors in two dimensions, which statements are correct?
a protractor and ruler can be used to draw the vectors with the correct angles and magnitudes, so that the resultant vector can then be measured.
the resultant vector always points from the tip of the first vector to the tail of the last vector.
the vectors can be added, then subtracted as if they were in one dimension, then these results averaged for the two dimensional sum.
the resultant always points from the tail of the first vector to the tip of the final vector.
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Explanation:

• Option 1: In the graphical method of vector addition (tail - to - tip method), a protractor is used to measure angles and a ruler is used to measure the magnitude of vectors (by using a scale, e.g., \(1\space cm = 1\space N\)). After constructing the vectors, the resultant vector (the vector that represents the sum of the given vectors) can be measured using the same ruler and protractor.
• Option 2: The resultant vector in the tail - to - tip method of vector addition points from the tail of the first vector to the tip of the last vector. So, the statement "The resultant vector always points from the tip of the first vector to the tail of the last vector" is incorrect.
• Option 3: Vectors in two - dimensions are added by resolving them into their \(x\) and \(y\) components (\(\vec{A}=A_x\hat{i}+A_y\hat{j}\), \(\vec{B}=B_x\hat{i}+B_y\hat{j}\), \(\vec{R}=(A_x + B_x)\hat{i}+(A_y + B_y)\hat{j}\)). They are not added and subtracted in one - dimension and then averaged.
• Option 4: According to the tail - to - tip rule of vector addition (if we have vectors \(\vec{A},\vec{B},\vec{C}\), we place the tail of \(\vec{B}\) at the tip of \(\vec{A}\) and the tail of \(\vec{C}\) at the tip of \(\vec{B}\)), the resultant vector \(\vec{R}=\vec{A}+\vec{B}+\vec{C}\) points from the tail of \(\vec{A}\) (the first vector) to the tip of \(\vec{C}\) (the last vector)

Answer:

A. A protractor and ruler can be used to draw the vectors with the correct angles and magnitudes, so that the resultant vector can then be measured.
D. The resultant always points from the tail of the first vector to the tip of the final vector.