How do you find the component form of v given its magnitude 5/2 and the angle it makes with the positive x-axis is #theta=45^circ#?

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Answer 1 · 2017-11-20T21:11:00

#color(blue)((5sqrt(2))/4hati+(5sqrt(2))/4hatj)#

If vector #v# forms an angle of #45^o# with the #x# axis, then:

#tan(45^o)=1#

This means that a component form vector will be of the form:

#ahati +bhat(j)# where #a=b#

We now need to find a unit vector in the direction of #v#.

This is:

#v_2= v_1/(||v_1||)#

We will use #hati+hatj# for #v_1#

#:.#

#v_2=(1+1)/(||1+1||)#

#||1+1||)=sqrt(2)#

So unit vector in direction of #v# is:

#1/sqrt(2)*(hati+hatj)#

For the given magnitude of we multiply the vector by#5/2#:

#5/2 * 1/sqrt(2) * (hati+hatj) = 5/(2sqrt(2)) * (hati+hatj)=color(blue)((5sqrt(2))/4hati+(5sqrt(2))/4hatj)#