\vec{v} \cdot \vec{w} = 3x + (-2)(4) + x(-1) = 3x - 8 - x = 2x - 8

Thu, 07 May 2026 10:21:31 +0000

# Understanding the Dot Product: ec{v} ÃƒÂ‚Ã‚Â· ec{w} = 3x + (-2)(4) + x(-1) = 2x ÃƒÂ¢Ã‚Â€Ã‚Â“ A Step-by-Step Guide When studying vectors in linear algebra, one essential operation is the dot product, denoted as \(ec{v} \cdot ec{w}\). The dot product is a powerful mathematical tool used in physics, computer graphics, engineering, and data science. In this article, weÃƒÂ¢Ã‚Â€Ã‚Â™ll walk through a clear derivation of the expression:
\[
ec{v} \cdot ec{w} = 3x + (-2)(4) + x(-1) = 3x - 8 - x = 2x - 8
\]
and explain how this simplifies using the definition of the dot product. --- ## What is the Dot Product \(ec{v} \cdot ec{w}\)?