If the x component of a vector a ,in the xy plane , is half as large as he magnitude of the vector , find the tangent of the angle between the vector and the x axis ?

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Answer 1 · 2018-01-31T14:07:24

#sqrt 3#

Suppose,the #a # vector makes an angle #theta# w.r.t the #X# axis,

so,its X component becomes #a cos theta#

Now,given, #acos theta=a/2#

so, #theta = 60#

#tan 60 = sqrt3#

Answer 2 · 2018-01-31T14:13:38

#"details has been showed below."#

enter image source here

#(OE)^2=(EB)^2+(OB)^2#
#(2x)^2=(EB)^2+x^2#

#(EB)^2=4x^2-x^2#

#(EB)^2=3x^2#
#sqrt((EB)^2)=sqrt(3x^2)#

#EB=x sqrt(3)#

#tan theta=bar (EB)/bar(OB)#

#tan theta=(cancel(x) sqrt (3))/cancel(x)#

#tan theta=sqrt (3)#