Solve {l}{|a|=sqrt{3^2+4^2}=5}{a+b=3hat{i}+4hat{j}+2hat{i}+2hat{j}-hat{k}=5hat{i}+6hat{j}-hat{k}}

$$\left. \begin{array} { l } { | a | = \sqrt { 3 ^ { 2 } + 4 ^ { 2 } } = 5 } \\ { a + b = 3 \hat { i } + 4 \hat { j } + 2 \hat { i } + 2 \hat { j } - \hat { k } = 5 \hat { i } + 6 \hat { j } - \hat { k } } \end{array} \right.$$

Solve for a

$$a=-5$$

$$a=5$$

Steps Using Definition of Absolute Value

Calculate 3 to the power of 2 and get 9.

$$|a|=\sqrt{9+4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$|a|=\sqrt{9+16}$$

Add 9 and 16 to get 25.

$$|a|=\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$|a|=5$$

Use the definition of absolute value.

$$a=5 a=-5$$