# Activity to resolve physical vectors.

1. Sum of vectors: method of the parallelogram. Given the vectors A **** and **B** * * as shown in Figure 1: ![](//blob.todoexpertos.com/uploads/md/60df085f3e30a90c537b183f7928db59.jpg) R= A^2+B^2}+2ABcosØ R= 5^2+8^2}+2(5)(8)(0.615661) R= 25+64+49.25 R= 138.24 R= 11.75810 It is here where I do not understand you, Figure 1. Scheme in the coordinate plane in two dimensions of the vectors **** and **B****. 1\.(a) Calculate **|C|** Given the vectors A **** and **B** * * as shown in Figure 2: ![](//blob.todoexpertos.com/uploads/md/6ffcb5d819a792c4b74e3185c31d3cf9.jpg) Figure 2. Scheme in the coordinate plane in two dimensions of the vectors ****, ** * * B** and **C**. 1\.b) finally, calculate **C** given the vectors A **** and **B.** as Well as the law of cosines (in particular in our case, the formula is **C^2** = **^**2 + ** B^**2 – 2** AB** Cosy).

2voto

Anon User Points 0

\begin{align}& \end{align}Luis,

In respect of the exercise 1, you are prompted to do so by the method of the parallelogram (which is totally graphic). For this you should draw a parallel to the vector B through the end of and parallel to the vector that passes through the endpoint of B, where we join the two parallel will be the result.

To do this analytically, in the case of sum of vectors I think the best thing is to do it in cartesian coordinates.


\begin{align}&A_x = |A| \cos \theta = 5 \cos(52°) = 3.08\\&A_y = |A| sin \theta = 5 sin(52°)=3.94\\&B_x = |B| \cos(0°) = 8\\&B_y = |B sin(0°) = 0\\&R_x = A_x + B_x = 3.08 + 8 = 11.08\\&R_y = A_y + B_y = 3.94 + 0 = 3.94\\&\text{you Already have the result, in case you want to calculate in polar}\\&|R| = \sqrt{R_x^2+R_y^2}=\sqrt{11.08^2+3.94^2}=11.76 \text{ (which effectively matches what your did you figure)}\\&\theta _R= arctan \bigg( \frac{R_y}{R_x}\bigg) = arctan \bigg( \frac{3.94}{11.08}\bigg) = 19.57°\end{align}In the second I don't understand that you ask, because for the module of the result reached with what you're considering, the issue is that I do not see the numeric values...

Salu2

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