A two-dimensional vector is a geometrical object that can be given either as a magnitude and direction, or as two components. When the two components are given, as in this problem, the magnitude and direction can be determined by using Pythagorean Theorem.

The *x*- and *y*- components of the vector, together with the vector itself, form a right triangle, in which the vector is the hypotenuse. The length of the hypotenuse is the magnitude of the vector. It equals

`A = sqrt(A_x^2 + A_y^2) = sqrt(5.7^2 + 3.4^2)= 6.6`

The direction is usually given as an angle that the vector makes with the *x*-axis. This angle is adjacent to the *x-*component and opposite to the *y-*component. Then, it equals to the inverse tangent (arctangent) of the ratio of the components.

`tan^(-1)(A_y/A_x) = tan^(-1)(3.4/5.7) = 31` degrees.

Therefore, the given vector A has the magnitude of 6.6 units and it makes the angle of 31 degrees with the positive direction of *x*-axis.

**Further Reading**

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