Question #4626a

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Answer 1 · 2017-12-07T16:15:01

The vector is #=5(cos(-53.1^@)hati+sin(-53.1^@)hatj)#. The unit vector in the same direction is #=(3/5hati-4/5hatj)#

Let #vecA=3hati-4hatj=r(costhetahati-sinthetahatj)#

The modulus of #vecA# is

#||vecA||=sqrt((3^2)+(-4)^2)=sqrt(9+16)=sqrt25=5#

Therefore,

#vecA=5(3/5hati-4/5hatj)#

So,

#costheta=3/5# and #sintheta=-4/5#

The angle theta is in the #4th# quadrant and

#theta=-53.1^@#

The unit vector in the same direction is

#hatA=(3/5hati-4/5hatj)#