If `vec(a) = hat(i) + 2 hat(j) + 3 hat(k)` and `vec(b) = 2 hat(i) + 3 hat(j) + hat(k)` , find a unit vector in the direction of `( 2 vec(a) + vec(b))`.

Explanation

Let `vec( c) = 2 vec(a) + vec(b) = 2( hat(i) + 2 hat(j) + 3 hat(k)) + ( 2 hat (i) + 3 hat(j) + hat(k))`
` = 4 hat(i) + 7 hat(j) + 7 hat(k)`
`| vec(c )| = sqrt(4^(2) + 7^(2) + 7^(2)) = sqrt(114)`
`hat(c ) = (vec( c))/(|vec( c)|) = ( 4 hat(i) + 7 hat(j) + 7 hat(k))/(sqrt(114))`