Question #a180c

2 Answers
Jul 2, 2017

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]

Jul 2, 2017

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