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#