Write two different vectors having same direction.

Explanation

Let `vec(a)=(hat(i)+hat(j)+hat(k)) and vec(b) = (2hat(i)+2hat(j)+2hat(k))`.
For Ist vector `vec(a)=hat(i)+hat(j)+hat(k)`
Comparing with `A=xhat(i) +yhat(j)+zhat(k)`, we get `x=1,y=1,z=1`
The direction cosines of a are given by `l=(1)/(sqrt(1^2+1^2+1^2))=(1)/(3),m=(1)/(sqrt(1^2+1^2+1^2))=(1)/(sqrt(3)) and n=(1)/(sqrt(1^2+1^2+1^2))=(1)/(3)`
Similarly, the direction cosines of b are given by `l=(2)/(sqrt(2^2+2^2+2^2))=(2)/(2sqrt(3))=(1)/(sqrt(3)),m=(2)/(sqrt(2^2+2^2+2^2))=(2)/(2sqrt(3))=(1)/(sqrt(3))`
and `n=(2)/(sqrt(2^2+2^2+2^2))=(2)/(2sqrt(3))=(1)/(sqrt(3))`.
Here, we see that both have same direction cosines.