Find the direction cosines of the following vectors: `2 hat i+2 hat j- hat k` `6 hat i-2 hat j-3 hat k` `3 hat i-4 hat k`

Explanation

(i)Let `vec{a}=2hat{i}+2 hat{j}- hat{k}`


`=2hat{i}+2 hat{j}- 1hat{k}`

Direction ratios are


`a=2, b=2, c=-1`

`text { Magnitude of } vec{a}=sqrt{2^{2}+2^{2}+(-1)^{2}} `

`qquad|vec{a}|=sqrt{4+4+1}=sqrt{9}=3`

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