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Find the unit vector of 4hati-3hatj+hatk...

Find the unit vector of `4hati-3hatj+hatk.`

A

`(hat4-3hatj+hatk)/sqrt(2)`

B

`(hat4-3hatj+hatk)/sqrt(26)`

C

`(hat4-4hatj+hatk)/sqrt(2)`

D

`(hat2-3hatj+hatk)/sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
We know that , for unit vector `A=A_(x)hati+A_(y)hatj+A_(z)hatk`
`=4hati-3hatj+hatk`
`therefore A_(x)=4,A_(y)=-3,A_(z)=1`
`|A|=sqrt(A_(x)^(2)+A_(y)^(2)+A_(x)^(2))=sqrt((4)^(2)+(-3)^(2)+(1)^(2))=sqrt(26)`
`therefore "Unit vector", hatA=(A)/(|A|)=(hat4-3hatj+hatk)/sqrt(26)`
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