Engineering Calculus Notes 48

# Engineering Calculus Notes 48 - 36 CHAPTER 1 COORDINATES...

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36 CHAPTER 1. COORDINATES AND VECTORS We read off its direction vector as −→ v 3 = 3 −→ ı + −→ + −→ k which is clearly not a scalar multiple of the other two. This tells us immediately that 3 is different from both 1 and 2 (it has a different direction). Let us ask whether 2 intersects 3 . It might be tempting to try to answer this by looking for a solution of the vector equation −→ p 2 ( t ) = −→ p 3 ( t ) but this would be a mistake . Remember that these two parametrizations describe the positions of two points—one moving along 2 and the other moving along 3 —at time t . The equation above requires the two points to be at the same place at the same time —in other words, it describes a collision . But all we ask is that the two
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