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If vec(A)= 2hat(i)+4hat(j)-5hat(k) then ...

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

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)`

Text Solution

Verified by Experts

The correct Answer is:
A
`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)`
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