Vector Combinations

#639 / Math Easy

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,

$$$V-W=(2-7)\mathbf{i}+(-3-1)\boldsymbol{j}+(5-(-9))\boldsymbol{k}$$$

$$$=-5\mathbf{i}-4\boldsymbol{j}+14\boldsymbol{k}$$$