Problema Solution
If the x component of a vector A→ , in the xy plane, is half as large as the magnitude of the vector, the tangent of the angle between the vector and the x axis is
Answer provided by our tutors
Let the vector be A = (x1, y1).
x1 = (1/2)√(x1^2 + y1^2)
4x1^2 = x1^2 + y1^2
3x1^2 = y1^2
x1^2 = y1^2/3
(y1/x1)^2 = 3
y1/x1 = √3
The tangent of 'a', the angle between the vector A and x-axis, is:
tan a = y1/x1
tan a = √3
The tangent of the angle between the vector and the x-axis is √3.