Question

Find a unit vector parallel to the resultant of the vectors A= 2i+3j+4k and B=3i+5j+k

Answer 1

$\sf{\large{\underline{\underline{EXPLANATION:}}}}$

Resultant of vectors A and B is given by,,

A+B=5i+8j+5k

Now using,,

$\mathtt{\blue{A+B=(|A+B|)(Â+B^)}}$

We get,,

Unit vector parallel to A+B,,

$\mathtt{\to{Â+B^=\frac{A+B}{|A+B|}}}$

$\mathtt{\to{Â+B^=\frac{5i+8j+5j}{\sqrt {5^{2}+8^{2}+5^{2}}}}}$

$\mathtt{\to{Â+B=\frac{5i+8j+5k}{\sqrt {114}}}}$

$\mathtt{\to{Â+B=\frac{5i}{\sqrt {114}}+\frac{8j}{\sqrt {114}}+\frac{5k}{\sqrt {114}}}}$

$\rule{200}2$

Hope it helps ❣️❣️❣️