Question

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 ?

Answer 1

`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`

Answer 2

`"details has been showed below."`

Explanation:

• 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)`