1. Find Direction cosines of a vector
`A=(1,2,2)`

Solution:
Here `vec A=(1,2,2)`

1. Calculate the magnitude(length) of vector `vec A`

`|vec A|`

`=sqrt(A_1^2 + A_2^2 + A_3^2)`

`=sqrt(1^2 + 2^2 + 2^2)`

`=sqrt(1 + 4 + 4)`

`=sqrt(9)`

`=3`


2. Calculate the direction cosines of vector `vec A`

`cos alpha=(A_1)/(|vec A|)=1/3`

`cos beta=(A_2)/(|vec A|)=2/3`

`cos gamma=(A_3)/(|vec A|)=2/3`

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2. Find Direction cosines of a vector
`A=(3,4)`

Solution:
Here `vec A=(3,4)`

1. Calculate the magnitude(length) of vector `vec A`

`|vec A|`

`=sqrt(A_1^2 + A_2^2)`

`=sqrt(3^2 + 4^2)`

`=sqrt(9 + 16)`

`=sqrt(25)`

`=5`


2. Calculate the direction cosines of vector `vec A`

`cos alpha=(A_1)/(|vec A|)=3/5`

`cos beta=(A_2)/(|vec A|)=4/5`

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