Given vector u = ⟨1, StartRoot 3 EndRoot⟩ and v = ⟨1, –1⟩, how are the vectors related?

The vectors form an acute angle of approximately 75°.
The vectors form an acute angle of approximately 81°.
The vectors form an obtuse angle of approximately 99°.
The vectors form an obtuse angle of approximately 105°.

When two straight lines or rays intersect at a shared endpoint, an angle is generated. The vectors form an obtuse angle of approximately 105°. Thus, the correct option is D.

What is an angle?

When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."

The angle between vector u and the positive x-coordinate is,

tan(θ) = √3 / 1

tan(θ) = √3

θ = 60°

The angle between vector v and the positive x-coordinate is,

tan(θ) = -1 / 1

tan(θ) = -1

θ = -45°

Now the angle between the two vectors is,

Angle = 60° + 45°

= 105°

Hence, The vectors form an obtuse angle of approximately 105°. Thus, the correct option is D.

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