Vector Combinations
Consider the two vectors shown. First find
V
+
W
, then solve for
V
-
W
.
Expand Hint
Vector addition is the operation of adding two or more vectors together into a vector sum. The so-called parallelogram law gives the rule for vector addition of two or more vectors.
$$$A+B=(a_x+b_x)\mathbf{i}+(a_y+b_y)\boldsymbol{j}+(a_z+b_z)\boldsymbol{k}$$$
where
$$A=a_x\textbf{i}+a_y\textbf{j}+a_z\textbf{k}$$
and
$$B=b_x\textbf{i}+b_y\textbf{j}+b_z\textbf{k}$$
.
Hint 2
Vector subtraction is the operation of subtracting one vector from another.
$$$A-B=(a_x-b_x)\mathbf{i}+(a_y-b_y)\boldsymbol{j}+(a_z-b_z)\boldsymbol{k}$$$
Vector addition is the operation of adding two or more vectors together into a vector sum. The so-called parallelogram law gives the rule for vector addition of two or more vectors.
$$$A+B=(a_x+b_x)\mathbf{i}+(a_y+b_y)\boldsymbol{j}+(a_z+b_z)\boldsymbol{k}$$$
where
$$A=a_x\textbf{i}+a_y\textbf{j}+a_z\textbf{k}$$
and
$$B=b_x\textbf{i}+b_y\textbf{j}+b_z\textbf{k}$$
. Thus,
$$$V+W=(2+7)\mathbf{i}+(-3+1)\boldsymbol{j}+(5-9)\boldsymbol{k}$$$
$$$=9\mathbf{i}-2\boldsymbol{j}-4\boldsymbol{k}$$$
Vector subtraction is the operation of subtracting one vector from another.
$$$A-B=(a_x-b_x)\mathbf{i}+(a_y-b_y)\boldsymbol{j}+(a_z-b_z)\boldsymbol{k}$$$
Thus,
$$$V-W=(2-7)\mathbf{i}+(-3-1)\boldsymbol{j}+(5-(-9))\boldsymbol{k}$$$
$$$=-5\mathbf{i}-4\boldsymbol{j}+14\boldsymbol{k}$$$
- $$V+W=9\mathbf{i}-2\boldsymbol{j}-4\boldsymbol{k}$$
- $$V-W=-5\mathbf{i}-4\boldsymbol{j}+14\boldsymbol{k}$$
Time Analysis
See how quickly you looked at the hint, solution, and answer. This is important for making sure you will finish the FE Exam in time.- Hint: Not clicked
- Solution: Not clicked
- Answer: Not clicked
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