# Question a180c

Jul 2, 2017

Unit Vecor of $\left(A + B\right)$ is $0.94 i + 0.34 j$

#### Explanation:

A= 8i +5j ; B = 3i-j#

$A + B = \left(8 i + 3 i\right) + \left(5 j - j\right) = 11 i + 4 j$

Magnitude of the vector $\left(A + B\right)$ is $\sqrt{{11}^{2} + {4}^{2}} = 11.7047$

Unit Vecor of $\left(A + B\right)$ is $\frac{11}{11.7047} i + \frac{4}{11.7047} j \mathmr{and} 0.94 i + 0.34 j$

Unit Vecor of $\left(A + B\right)$ is $0.94 i + 0.34 j$ [Ans]

Jul 2, 2017

#### Explanation:

Let $A = 8 i + 5 j$ and $B = 3 i - j$.
$A + B = \left(8 + 3\right) i + \left(5 - 1\right) j$
$= 11 i + 4 j$
The magnitude of $A + B$ is
$| | A + B | | = \sqrt{{11}^{2} + {4}^{2}} = \sqrt{121 + 16} = \sqrt{137}$
The unit vector has magnitude 1. Divide $A + B$ by its magnitude. This means multiplying by the reciprocal of $\sqrt{137}$.
$u = \frac{| | A + B | |}{\sqrt{137}} = \frac{11}{\sqrt{137}} i + \frac{4}{\sqrt{137}} j$