09.19 - [Collect summaries of section 10.6[Collect...

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Unformatted text preview: [Collect summaries of section 10.6] [Collect diagnostic quiz #2] [Hand out time-sheets for assignment #3] Section 10.5: Equations of lines and planes Main ideas: • Three ways to describe a line: ..?.. o Vector (parametric) equations: r = [ O → P ] + t d , with P a point on the line and d a direction vector pointing in the direction of the line o Symmetric equations: ( x – x ) / a = ( y – y ) / b = ( z – z ) / c , where 〈 x , y , z 〉 is a point on the line and 〈 a , b , c 〉 determines which way the line points o Two-point vector equation: r = [ O → P ] + t [ P → Q ], with P , Q points on the line • Three ways to describe a plane: ..?.. o Vector equation: n • ( r – [ O → P ]) = 0, with P a point on the plane and n a normal vector (note that it can also be written n • r = n • [ O → P ] o Scalar equation: ax + by + cz + d = 0 o Parametric equations: r = [ O → P ] + t a + s b ....
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09.19 - [Collect summaries of section 10.6[Collect...

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