Question

Question #a180c

Answer 1

Unit Vecor of `(A+B)` is `0.94i +0.34j`

Explanation:

`A= 8i +5j ; B = 3i-j`

`A+B = (8i+3i) + ( 5j -j) = 11i+ 4j`

Magnitude of the vector `(A+B)` is `sqrt(11^2+4^2) =11.7047`

Unit Vecor of `(A+B)` is `11/11.7047i + 4/11.7047 j or 0.94i +0.34j`

Unit Vecor of `(A+B)` is `0.94i +0.34j` [Ans]

Answer 2

The exact answer...

Explanation:

Let `A = 8i + 5j` and `B = 3i - j`.
Then we add the vectors by adding their components.
`A + B = (8 + 3)i + (5 - 1)j`
`= 11i + 4j`

The magnitude of `A + B` is
`||A + B|| = sqrt(11^2 + 4^2) = sqrt(121 + 16) = sqrt(137)`

The unit vector has magnitude 1. Divide `A + B` by its magnitude. This means multiplying by the reciprocal of `sqrt(137)`.

`u = (||A + B||)/(sqrt(137)) = 11/sqrt(137)i + 4/sqrt(137)j`