Adding Vectors $\overrightarrow { \mathrm { A } }$ And $\vec { B }$

question 15

Multiple Choice

Adding vectors $\overrightarrow { \mathrm { A } }$ and $\vec { B }$ by the graphical method gives the same result for $\overrightarrow { \mathrm { A } }$ + $\vec { B }$ and $\vec { B }$ + $\overrightarrow { \mathrm { A } }$
If both additions are done graphically from the same origin,the resultant is the vector that goes from the tail of the first vector to the tip of the second vector,i.e,it is represented by a diagonal of the parallelogram formed by showing both additions in the same figure.Note that a parallelogram has 2 diagonals.Keara says that the sum of two vectors by the parallelogram method is $\overrightarrow { \mathbf { R } } = 5 \hat { \mathbf { i } }$
Shamu says it is $\overrightarrow { \mathbf { R } } = \hat { \mathbf { i } } + 4 \hat { \mathbf { j } }$
Both used the parallelogram method,but one used the wrong diagonal.Which one of the vector pairs below contains the original two vectors?

• A) \[\overrightarrow { \mathbf { A } } = - 3 \hat { \mathbf { i } } - 2 \hat { \mathbf { j } }\] ; \(\overrightarrow { \mathbf { B } } = - 2 \hat { \mathbf { i } } - 2 \hat { \mathbf { j } }\)
• B) \(\overrightarrow { \mathbf { A } } = + 3 \hat { \mathbf { i } } - 2 \hat { \mathbf { j } }\) ; \(\overrightarrow { \mathbf { B } } = - 2 \hat { \mathbf { i } } + 2 \hat { \mathbf { j } }\)
• C) \(\overrightarrow { \mathbf { A } } = - 3 \hat { \mathbf { i } } - 2 \hat { \mathbf { j } }\) ; \(\overrightarrow { \mathbf { B } } = + 2 \hat { \mathbf { i } } + 2 \hat { \mathbf { j } }\)
• D) \[\overrightarrow { \mathbf { A } } = + 3 \hat { \mathbf { i } } - 2 \hat { \mathbf { j } }\] ; \[\overrightarrow { \mathbf { B } } = + 2 \hat { \mathbf { i } } - 2 \hat { \mathbf { j } }\]
• E) \[\overrightarrow { \mathbf { A } } = + 3 \hat { \mathbf { i } } + 2 \hat { \mathbf { j } }\] ; \(\overrightarrow { \mathbf { B } } = - 2 \hat { \mathbf { i } } + 2 \hat { \mathbf { j } }\)

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