If $\vec A=2\vec i+4\vec j-\vec k$, $\vec B=2\vec i-3\vec j+\vec k$ and $\vec C=- \vec i+3\vec j$, then unit vector in direction of $\vec A+\vec B+\vec C$. I tried to find unit vector of all vectors and to add all of them. But I didn't get correct answer. It's a competitive question. I am unable to get the correct answer. I added unit vector of all vectors then got unit vector.
$$\frac1{\sqrt{21}}\vec A=\frac1{\sqrt{21}}(2\vec i+4\vec j-\vec k)$$ $$\frac1{\sqrt{14}}\vec B=\frac1{\sqrt{21}}(2\vec i-3\vec j+\vec k)$$ $$\frac1{\sqrt{10}}\vec C=\frac1{\sqrt{21}}(-\vec i+3\vec j)$$ Now what I should do to get the correct answer?
You should first add the vectors $\vec A, \vec B$ and $\vec C$, and then calculate the unit vector.
$$\vec{A} + \vec B + \vec C = 3\hat\imath + 4\hat\jmath$$ $$\text{Unit vector }= (3/5)\hat\imath + (4/5)\hat\jmath$$