# Find a unit vector parallel to the sum of the vector a =2i+4j-5k and b= i+2j+3k?

First of all find the sum of the given two vectors $$\vec{a}=2i +4j-5k,\:and\:\vec{b}=i +2j+3k$$

That is $$\vec{ a}+\vec{b}=3i+6j-2k$$

$$|\vec{a}+\vec{b}|=\sqrt{3^2+6^2+(-2)^2}=\sqrt{9+36+4}=\sqrt{49}=7$$

Unit vector along $\vec{a}+\vec{b}=\Large \frac{\vec{a}+\vec{b}}{|\vec{a}+\vec{b}|}$$=\large\frac{1}{7}$$(3i+6j-2k)$
edited Jun 3, 2013