MATM1544_lecture 21.pdf - The image part with relationship ID rId7 was not found in the file MATM1544 LECTURE 21 The vector equation of a line September

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9/2/2015 1 The image part with relationship ID rId7 was not found in the file. T: +27(0)51 401 9111 | [email protected] | MATM1544 LECTURE 21 The vector equation of a line September 2, 2015 T: 051 401 9111 [email protected] CONTENT Vector equation of a line Parametric equations of a line Examples Exercise
9/2/2015 2 RECAP THE VECTOR EQUATION OF A LINE ° = ° ± + ²³ ³ : Vector on or parallel to the line. ° ± : Any point on the line with position vector ° ± . °: General point (x, y, z) on line with position vector ° . ²: Parameter where −∞ < ´ < ∞ Then ° = ° ± + ²³ . PARAMETRIC EQUATIONS OF A LINE If the point on the line has a position vector b ° = µ + ²³ We get ° = · ¸ = µ ¹ µ º µ » + ² ³ ¹ ³ º ³ » = µ ¹ + ²³ ¹ µ º + ²³ º µ » + ²³ » or ¶ = µ ¹ + ²³ ¹ · = µ º + ²³ º ¸ = µ » + ²³ » Parametric equations of the line.
9/2/2015 3 EXAMPLE Example 1. The point (1,2,1) is on a certain line, which is parallel to the vector (1, −3, 1) . (a) Find the vector equation of the line. (b) Find the parametric equations of the line.

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• Summer '20
• Parametric equation, vector equation of a line

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