Transcribed Image Text:**Title: Finding Orthogonal Vectors**
**Objective:**
Determine all vectors **v** that are orthogonal to **u**.
**Problem Statement:**
Given a vector **u = (6, 1, 0)**, find vectors **v = (v₁, v₂, v₃)** that are orthogonal to **u**.
**Instructions:**
1. Set \( v_1 = t \) and \( v_3 = s \).
2. Solve for \( v_2 \) in terms of \( t \) and \( s \).
There is a structure included for vector **v**:
- The vector **v** is represented as **v = (□, v₂, □)**, indicating places to fill in values.
The process requires using the orthogonality condition, which states that the dot product **u • v = 0**. Use this condition to solve for \( v_2 \).
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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