If `vec(A)= 2hat(i)+4hat(j)-5hat(k)` then the direction of cosins of the vector `vec(A)` are

Options

A. `(2)/(sqrt45), (4)/(sqrt45) and (-5)/(sqrt45)`
B. `(1)/(sqrt45), (2)/(sqrt45) and (3)/(sqrt45)`
C. `(4)/(sqrt45), 0 and (4)/(sqrt45)`
D. `(3)/(sqrt45),(2)/(sqrt45) and (5)/(sqrt45)`

Answer

A

Explanation

`vec(A)= (A cos alpha) hat(i) + (A cos beta) hat(j) + (A cos gamma) hat(k)= A_(x) hat(i) + A_(y) hat(j) + A_(z) hat(k)`
`cos alpha= (A_(x))/(A) , cos beta= (A_(y))/(A), cos gamma= (A_(z))/(A)`
Since, `vec(A) = 2hat(i) + 4hat(j) - 5hat(k) , |vec(A)|= A= sqrt(2^(2) + 4^(2) + (-5)^(2))= sqrt45`
`cos alpha= (2)/(sqrt45), cos beta= (4)/(sqrt45), cos gamma= (-5)/(sqrt45)`