Problems

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Angle Between 3D Vectors

3D Geometry

Medium

Compute the angle (in radians) between two 3D vectors v and w. Return $θ∈[0,π]$ Handle zero vectors gracefully.

Angle Formula:

\cos\theta = \frac{v \cdot w}{\lVert v \rVert \, \lVert w \rVert} \\ \theta = \arccos(\cos\theta)

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Examples

Input: v = [1, 0, 0], w = [0, 1, 0]

Output: ≈ 1.571 (π/2)

Input: v = [1, 2, 3], w = [2, 4, 6]

Output: ≈ 0.0

Hint 1

Check if either norm <10⁻¹⁰, if so return np.nan.

Hint 2

Use np.clip() before np.arccos() to avoid numerical errors.

Requirements

Inputs: v,w as lists or arrays of shape (3,)
Return scalar float: angle in radians
Use dot product and norms
Clamp cosine value to [−1,1] before arccos
If either vector has zero norm: return np.nan

Constraints

Absolute error tolerance: 10⁻⁶
NumPy only; time limit: 200ms

Try Similar Problems

Normalize 3d Vector Norm 3d Dot Product Rotate Around Z Homogeneous Transform

Angle Between 3D Vectors

3D Geometry

Medium

Compute the angle (in radians) between two 3D vectors v and w. Return $θ∈[0,π]$ Handle zero vectors gracefully.

Angle Formula:

\cos\theta = \frac{v \cdot w}{\lVert v \rVert \, \lVert w \rVert} \\ \theta = \arccos(\cos\theta)

Loading visualization...

Examples

Input: v = [1, 0, 0], w = [0, 1, 0]

Output: ≈ 1.571 (π/2)

Input: v = [1, 2, 3], w = [2, 4, 6]

Output: ≈ 0.0

Hint 1

Check if either norm <10⁻¹⁰, if so return np.nan.

Hint 2

Use np.clip() before np.arccos() to avoid numerical errors.

Requirements

Inputs: v,w as lists or arrays of shape (3,)
Return scalar float: angle in radians
Use dot product and norms
Clamp cosine value to [−1,1] before arccos
If either vector has zero norm: return np.nan

Constraints

Absolute error tolerance: 10⁻⁶
NumPy only; time limit: 200ms

Try Similar Problems

Normalize 3d Vector Norm 3d Dot Product Rotate Around Z Homogeneous Transform

Case 1

Case 2

v =

Accepts: array

w =

Accepts: array