Question

Let a = i + 2j + 3k and b = 3i + j. Find the unit vector in the direction of a + b.

Answer 1

4i+4j is the unit vector in the direction of a+b

Answer 2

Answer: Unit vector in the direction of $\vec a+\vec b$

$\frac{4}{\sqrt{34} }\hat i +\frac{3}{\sqrt{34} }\hat j +\frac{3}{\sqrt{34} }\hat k$

Step-by-step explanation:

let

$\vec a=\hat i+2\hat j+3\hat k\\\\\vec b=3\hat i+\hat j\\\\\\\vec a+\vec b=\hat i+2\hat j+3\hat k+3\hat i+\hat j\\\\\\\vec a+\vec b=4\hat i+3\hat j+3\hat k$

so unit vector in the direction of

$\vec a+\vec b$

$|\vec a+\vec b|=\sqrt{4^{2}+3^{2}+3^{2}}\\\\=\sqrt{16+9+9}\\\\=\sqrt{34}$

So unit vector in the direction of   $\vec a+\vec b$  is

$= \frac{4}{\sqrt{34} }\hat i +\frac{3}{\sqrt{34} }\hat j +\frac{3}{\sqrt{34} }\hat k$