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 ?

2 Answers
Jan 31, 2018

sqrt 3

Explanation:

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

Jan 31, 2018

"details has been showed below."

Explanation:

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  • We can solve it using the EOB triangle .

(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)