# Chapter 3 - Vectors and Coordinates Systems - Exercises and Problems - Page 78: 26

$\vec D = 4.88\hat i + 2.80 \hat j$

#### Work Step by Step

We have $\vec A = 2sin(15^o) \hat i + 2cos(15^o) \hat j$ $\vec A = 0.52 \hat i + 1.92 \hat j$ and $\vec B = 4cos(15^o) \hat i - 4sin(15^o) \hat j$ $\vec B = 3.84 \hat i - 1.04 \hat j$ Now $\vec D = 2\vec A + \vec B$ $\vec D = 2( 0.52 \hat i + 1.92 \hat j) + 3.84 \hat i - 1.04 \hat j$ $\vec D = 1.04 \hat i + 3.84 \hat j + 3.84 \hat i - 1.04 \hat j$ $\vec D = 4.88\hat i + 2.80 \hat j$

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