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 (Figure 1.30 ). We have 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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