Vector v has a direction of (5,3) find the direction angle for v to the nearest degree

The direction of the path of the vector is measured relative to the

horizontal line or axis.

The direction angle for, v is approximately 31°.

Reasons:

The given vector can be expressed as follows;

v = 5·i + 3·j

Therefore, the vector extends 5 units in the x-direction and 3 units in the y-

direction.

The tangent of the angle, θ, formed by the direction of the vector, which is

the angle of the direction of the vector, is given as follows;

Which gives;

T

The direction angle for the vector, v, to the nearest degree θ ≈ 31°

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Step-by-step explanation:

We have been given that vector v has a direction of (5,3). We are asked to find direction angle for v to nearest degree.

We know that direction of vector with components can be determined by .

Upon substituting the components of given vector in above formula, we will get:

Upon rounding to nearest degree, we will get:

Therefore, the direction angle for vector v is 31 degrees.