Engineering Calculus Notes 64

Engineering Calculus Notes 64 - Q to a point R on the line...

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52 CHAPTER 1. COORDINATES AND VECTORS These interpretations of the dot product make it a powerful tool for attacking certain kinds of geometric and mechanical problems. We consider two examples below, and others in the exercises. Distance from a point to a line: Given a point Q with coordinate vector −→ q and a line parametrized via −→ p ( t ) = −→ p 0 + t −→ v let us calculate the distance from Q to . We will use the fact that this distance is achieved by a line segment from
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Unformatted text preview: Q to a point R on the line such that QR is perpendicular to ℓ (Figure 1.30 ). We have ℓ b P b Q R −→ v → w Figure 1.30: Distance from Point to Line −−→ P Q = −→ q − −→ p . We will denote this, for clarity, by −→ w := −→ q − −→ p −−→ P R = proj −→ v −−→ P Q = proj −→ v −→ w so | P R | = −→ w · −→ v | −→ v |...
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