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Question

How to find the angle between the vector and x-axis?


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Solution

Calculation of angle between x-axis and vector:

Angle between vectors α=cos-1(a.b|a||b|).

x-axis is represented by i.

Let vector be xi+yj+zk

a.b=i.(xi+yj+zk)a.b=x[(i.i=1),(i.j=0),(i.k=0)]a=12[|v|=x2+y2+z2]a=1|b|=x2+y2+z2α=cos-1x1.x2+y2+z2

Therefore, the angle between the vector and x-axis is cos-1(x1.x2+y2+z2) .


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