Vector A has magnitude 3.7 units; vector B has magnitude 5.9. The angle between vector A and B is 45 degrees. What is the magnitude of vector A+ vector B?

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Answer 1 · 2017-12-07T12:57:04

Magnitude of #(vecA+vecB)# is #8.91# units at an angle
of #27.92^0# from #vecA#

Completing the parallelogram of #vec A and vec B# , the

diagonal represents represents resultant of two vectors

#vecA and vecB#. The angle between #vecA#and parallal

#vecB# is #180-45=135^0# By applying cosine law

we get magnitude of #|vecA+vecB|^2#

#= 3.7^2+5.9^2-2*3.7*5.9*cos135~~79.37# or

#|vecA+vecB|= 8.91# units . Let the resultant vector.

#|vecA+vecB|# makes an angle #theta# with #vecA#.

By sine law #5.9/sintheta=8.91/sin135 # or

#sin theta = (5.9*sin135)/8.91~~0.4682#

or #theta= sin^-1(0.4682)~~27.92^0# from #vecA#.

Magnitude of #(vecA+vecB)# is #8.91# units at an angle

of #27.92^0# from #vecA# [Ans]