Question

Given the vector v⃗ =⟨3–√,1⟩ ; find the direction angle of this vector.

A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 90 degrees

Answer 1

The direction angle of the given vector is approximately 30 degrees.

Step-by-step explanation:

The direction angle of a vector can be found by using the formula:

θ = tan-1(y/x)

where y is the vertical component of the vector and x is the horizontal component of the vector.

In this case, the vector v⃗ = ⟨3–√,1⟩ has a vertical component of 1 and a horizontal component of 3–√. Thus, the direction angle can be found as follows:

θ = tan-1(1/(3–√))

Simplifying the expression, we get:

θ ≈ 30°

Therefore, the direction angle of the vector is approximately 30 degrees.