Problem 2
Question
What is the dot product of two orthogonal vectors?
Step-by-Step Solution
Verified Answer
The dot product of two orthogonal vectors is 0.
1Step 1: Definition of Orthogonal Vectors
Two vectors are considered orthogonal or perpendicular to each other if the angle between them is 90 degrees. This property can be described mathematically by the dot product, where the dot product of two vectors \( \vec{a} \) and \( \vec{b} \) is defined as \( \vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos(\theta) \), where \( \theta \) is the angle between the vectors.
2Step 2: Dot Product of Orthogonal Vectors
For orthogonal vectors, the angle between the vectors is 90 degrees. The cosine of 90 degrees is 0. Therefore, the dot product between two orthogonal vectors equals 0 because \( \vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos(90^{\circ}) = 0 \), regardless of the length of the vectors.
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