Question

select all that apply
when adding vectors in two dimensions, which statements are correct?
the resultant vector always points from the tip of the first vector to the tail of the last vector.
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 always points from the tail of the first vector to the tip of the final vector.
the vectors can be added, then subtracted as if they were in one dimension, then these results averaged for the two dimensional sum.

Explanation:

• For the first statement: In vector addition (triangle or polygon method), the resultant vector points from the tail of the first vector to the tip of the last vector, not from the tip of the first vector to the tail of the last vector. So this statement is incorrect.
• For the second statement: In the graphical method of vector addition (using the parallelogram or triangle law), a protractor (to measure angles) and a ruler (to measure magnitudes according to a scale) are used. First, vectors are drawn with correct angles and magnitudes, and then the resultant vector's magnitude and direction (angle) are measured. So this statement is correct.
• For the third statement: By the triangle law of vector addition (if we have vectors \(\vec{A}\), \(\vec{B}\), \(\vec{C}\), \(\vec{R}=\vec{A}+\vec{B}+\vec{C}\)), when 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 \(\vec{R}\) points from the tail of \(\vec{A}\) to the tip of \(\vec{C}\). So this statement is correct.
• For the fourth statement: Vectors are not added and subtracted as one - dimensional scalars and then averaged. In two - dimensions, we use component methods (\(R_x = A_x + B_x+\cdots\), \(R_y=A_y + B_y+\cdots\) and \(R=\sqrt{R_x^{2}+R_y^{2}}\), \(\theta=\tan^{- 1}(\frac{R_y}{R_x})\)) or graphical methods (not the described incorrect arithmetic operation). So this statement is incorrect.

Answer:

B. 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.
C. The resultant always points from the tail of the first vector to the tip of the final vector.