For a classification problem PCA has been used to reduce the dimensionality of a feature space from 100 to 10.

Which of the following option is true about the angle b/w first 2 and 10th principal components?

The correct option is θ = 90.

Principal Component Analysis (PCA) is a dimensionality reduction technique that transforms a set of correlated variables into a set of linearly uncorrelated variables called principal components.

These principal components are defined by the eigenvectors of the data's covariance matrix. A fundamental mathematical property of symmetric matrices (such as the covariance matrix) is that their eigenvectors corresponding to distinct eigenvalues are orthogonal (perpendicular) to each other.

Because the principal components are orthogonal to one another, the angle between any two distinct principal components is always 90 degrees (or $\frac{\pi }{2}$ radians).

Therefore, the angle θ between the first, second, or tenth principal components (or any other pair of different principal components) is precisely 90 degrees:

$\theta =90$