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Unit vector parallel to the resultant of...

Unit vector parallel to the resultant of vectors `vec(A)= 4hat(i)-3hat(j)` and `vec(B)= 8hat(i)+8hat(j)` will be

A

`(24hat(i)+5hat(j))/(13)`

B

`(12hat(i)+5hat(j))/(13)`

C

`(6hat(i)+5hat(j))/(13)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Resutant of vectors `vec(A)` and `vec(B)`
`vec(R )= vec(A)+vec(B)= 4hat(i)-3hat(j)+8hat(i)+8hat(j)= 12hat(i)+5hat(j)`
`hat(R )= (vec(R ))/(|R|)= (12hat(i)+5hat(j))/(sqrt((12)^(2)+(5)^(2)))= (12hat(i)+5hat(j))/(13)`
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