# Given Vector A: 14.1i + 5.1j and Vector B: 15.0i + 26.0j. How do you add and subtract these two vectors?

Jul 1, 2016

$\vec{A} + \vec{B} = 29.1 i + 31.1 j$

$\vec{A} - \vec{B} = - 0.9 i - 20.9 j$.

#### Explanation:

Let Vector A be denoted by $\vec{A}$ and suppose that $\vec{A} = {a}_{1} i + {a}_{2} j$.

Suppose, $\vec{B} = {b}_{1} i + {b}_{2} j$.

Then, by defn. of Vector Addition, $\vec{A} + \vec{B} = \left({a}_{1} + {b}_{1}\right) i + \left({a}_{2} + {b}_{2}\right) j$.

Similarly, $\vec{A} - \vec{B} = \left({a}_{1} - {b}_{1}\right) i + \left({a}_{2} - {b}_{2}\right) j$.

Therefore, in our case, $\vec{A} + \vec{B} = 29.1 i + 31.1 j$ and, $\vec{A} - \vec{B} = - 0.9 i - 20.9 j$.