Find the direction cosines of the vector `hati +2hatj + 3hatk`

Explanation

Let `vec(a) =hat(i) +2hat(j)+3hat(k)`.
Then, `|vec(a)|=sqrt(1^2+2^2+3^2)=sqrt(14)`
`therefore hat(a) =(vec(a))/(|a|)rArr hat(a) =(1)/(sqrt(14))(hat(i)+2hat(j)+3hat(k))`.
`rArr hat(a) =(a)/(sqrt(14))hat(i)+(2)/(sqrt(14))hat(j)+(3)/(sqrt(14))hat(k)`.
Hence , direction cosines of the given vector are `(1)/(sqrt(4),(2)/(sqrt(14)),(3)/(sqrt(14))`.
( `because` Direction cosines are the coefficients of `hat(i),hat(j),hat(k)` of unit vector.)