Find a vector in the direction of vector `5hat(i)-hat(j)+2hat(k)` which has magnitude 8 unit.

Explanation

Let `vec(a)=5hat(i)-hat(j)+2hat(k)`.
Comparing with `X= x hat(i) -yhat(j)+zhat(k)`, we get `x=5,y=-1 z= 2`.
`therefore` Magnitude `|a|=sqrt(x^2+y^2+z^2)= sqrt(5^2+(-1)^2+2^2)=sqrt(25+1+4)=sqrt(30)`.
`therefore` Unit vector in the direction of given vector
`hat(a)=(a)/(|a|)=(5hat(i)-hat(j)+2hat(k))/(sqrt(30))`. required vector `=8hat(a)=8((5hat(i)-hat(j)+2hat(k))/(sqrt(30)))=(40)/(sqrt(30))hat(i)-(8)/(sqrt(30))hat(j)+(16)/(sqrt(30))hat(k)`.