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Problem Metadata

Date: November 14, 2025

Problem Number: #4

Problem Curator: @Phanie

lymphoidcell - Overview

Indonesian version:

Dot Product, Orthogonality, Distance, Angle, Projection in ℝ³/ℝ⁴

Category: Machine Learning Math - Linear Algebra

Difficulty Level: Beginner

Problem Statement

We will work with vectors in Euclidean space. Answer all parts.

(a) Dot Product Computation

Let $u = (2, -1, 4)$, $v = (-3, 5, 2)$, and $w = (1, 0, -6)$.

Compute:

$$ u ⋅ v $$

$$ u ⋅ w $$

$$ v ⋅ w $$

(b) Dot Product Using Column Vectors

Let