Question

Solve the following
r1=3i−2j+kr2=2i−4j−3kr3=−i+2j+2kFindr1r2

7
11
3
10

Answer 1

Answer on Question #46939 – Math – Vector Calculus

Solve the following

$$r1 = 3i - 2j + k \quad r2 = 2i - 4j - 3k \quad r3 = -i + 2j + 2k \text{ Find } r1 \quad r2$$

7

11

3

10

Solution:

$$\begin{array}{l} \ddot{r}_1 = 3\ddot{i} - 2\ddot{j} + \dddot{k} \\ \ddot{r}_2 = 2\ddot{i} - 4\ddot{j} - 3\ddot{k} \\ \ddot{r}_3 = -\ddot{i} + 2\ddot{j} + 2\ddot{k} \\ \end{array}$$

If the vectors are expressed in terms of unit vectors $i, j$, and $k$ along the $x, y$, and $z$ directions, the scalar (or dot) product can also be expressed in this form:

$$\ddot{r}_1 \ddot{r}_2 = r_{1x} r_{2x} + r_{1y} r_{2y} + r_{1z} r_{2z} = 3 \cdot 2 + (-2)(-4) + 1(-3) = 6 + 8 - 3 = 11$$

Answer: $\ddot{r}_1 \ddot{r}_2 = 11$

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