Question

luego (mal7525) - unit 1 hw3 25 - 26 - tejeda - (barre
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001 (part 1 of 2) 10.0 points
express the vector r
in terms of \\( \vec{a},\vec{b},\vec{c}, \\) and \\( \vec{d} ), the sides of a
parallelogram.

1. \\( \vec{r}=\vec{b}-\vec{a} \\)
2. \\( \vec{r}=\vec{d}-\vec{a} \\)
3. \\( \vec{r}=\vec{c}+\vec{d} \\)
4. \\( \vec{r}=\vec{a}+\vec{d} \\)
5. \\( \vec{r}=\vec{a}-\vec{d} \\)
6. \\( \vec{r}=\vec{b}+\vec{a} \\)
7. \\( \vec{r}=\vec{b}+\vec{d} \\)
8. \\( \vec{r}=\vec{a}-\vec{b} \\)
9. \\( \vec{r}=\vec{a}-\vec{c} \\)
10. \\( \vec{r}=\vec{c}+\vec{b} \\)

002 (part 2 of 2) 10.0 points
express the vector \\( \vec{p} \\) in terms of \\( \vec{a},\vec{b},\vec{c}, \\) and
\\( \vec{d} ).

1. \\( \vec{p}=\vec{a}-\vec{b} \\)
2. \\( \vec{p}=\vec{b}-\vec{a} \\)
3. \\( \vec{p}=\vec{b}-\vec{a} \\)
4. \\( \vec{p}=\vec{c}-\vec{a} \\)
5. \\( \vec{p}=\vec{b}+\vec{a} \\)
6. \\( \vec{p}=\vec{c}+\vec{b} \\)
7. \\( \vec{p}=\vec{a}+\vec{d} \\)
8. \\( \vec{p}=\vec{a}-\vec{b} \\)
9. \\( \vec{p}=\vec{c}+\vec{b} \\)
10. \\( \vec{p}=\vec{b}+\vec{d} \\)

003 1
vectors \\( \vec{a},\vec{b},\vec{c},\vec{d} \\) the figure

Explanation:

Step1: Use vector addition property

In a parallelogram, if we consider the vectors along the sides and diagonals. Let's start from the fact that to get from the starting - point of one side - vector to the end - point of the diagonal vector, we can use vector addition.
If we start from the tail of vector $\vec{A}$ and want to get to the tip of vector $\vec{R}$, and we know that we can move along $\vec{A}$ and then along $\vec{D}$.
By the triangle law of vector addition, $\vec{R}=\vec{A}+\vec{D}$.

Answer:

1. $\vec{R}=\vec{A}+\vec{D}$