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Find the unit vector of vec(A)=2hat(i)+3...

Find the unit vector of `vec(A)=2hat(i)+3hat(j)+2hat(k)`.

A

`(5hat(i)+2hat(j)+hat(k))/sqrt(30)`

B

`(2hat(i)-3hat(j)-2hat(k))/sqrt(15)`

C

`(2hat(i)+3hat(j)+2hat(k))/sqrt(17)`

D

`(2hat(i)-3hat(j)-2hat(k))/sqrt(17)`

Text Solution

Verified by Experts

The correct Answer is:
C
`vec(A)=2hati+3hatj+2hatk`
we know that `hat(A)=vec(A)/(|vec(A)|)`
where `|vec(A)|=sqrt(A_(x)^(2)+A_(y)^(2)+A_(z)^(2))`
`=sqrt(2^(2)+3^(2)+2^(2))=sqrt(4+9+4)= sqrt(17)`
`hat(A)= vec(A)/(|vec(A)|)=(2hat(i)+3hat(j)+2hat(k))/sqrt(17)`
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