Texts:
1. Let x and y be two unit norm vectors in R^2. The angle between these two vectors is 60 degrees. Find the Euclidean distance between the vectors x and y. [4 Marks]
2. Let v1, v2, and v3 be the eigenvectors of the matrix. Find v2 and v3. Here, v is the sum of the last two digits of your roll number. [4 Marks]
3. Consider a discrete-time signal having four samples given as x[0] = 1, x[1] = 2, x[2] = 2, x[3] = 1. Determine its discrete Fourier transform (DFT). Determine the dominating frequency that is present in this signal. [5 Marks]
4. Find the implicit representation of the following shapes:
a) A sphere of radius equal to 3 units and centered at the point (1, 1, 1).
b) A plane passing through three points (10, 0, 0), (1, 0), and (0, 0.1). [2 Marks] [2 Marks]
5. What is the point cloud representation of a 3D object? What is the effect of increasing or decreasing the number of points in a point cloud on the appearance of the object? [3 Marks]