A vector of magnitude 12 units in XY plane is making an angle of 120° with positive X-axis. Find that vector and also unit vector in the opposite of this vector?

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Answer 1 · 2018-06-20T16:32:45

The vector is #=<-6,6sqrt3> # and the unit vector in the opposite direction is #= <1/2, -sqrt3/2>#

Let the vector be #vecv#

Then,

#||vecv||=12#

The angle is #theta=120^@#

The components of the vector are

#v_x=12cos120=12*-1/2=-6#

#v_y=12sin60=12*sqrt3/2=6sqrt3#

The vector is #vecv= <-6,6sqrt3>#

The vector in the opposite direction is

#vecv_1= <6.-6sqrt3>#

The magnitude of this vector is

#||vecv_1||=sqrt((6)^2+(-6sqrt3)^2)=12#

The unit vector is

#hatv_1=vecv_1/(||vecv_1||)=1/12* <6,-6sqrt3>#

#= <1/2, -sqrt3/2>#