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Find the non-parametric form of vector equation and Cartesian equations of the plane rijksijktijkr→=(6i^-j^+k^)+s(-i^+2j^+k^)+t(-5i^-4j^-5k^) - Mathematics

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प्रश्न

Find the non-parametric form of vector equation and Cartesian equations of the plane `vec"r" = (6hat"i" - hat"j" + hat"k") + "s"(-hat"i" + 2hat"j" + hat"k") + "t"(-5hat"i" - 4hat"j" - 5hat"k")`

बेरीज
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उत्तर

`vec"a" = 6hat"i" - hat"j" + hat"k"`

`vec"b" = -hat"i" + 2hat"j" + hat"k"`

`vec"c" = -5hat"i" - 4hat"j" - 5hat"k"`

`vec"b" xx vec"c" = |(hat"i", hat"j", hat"k"),(-1, 2, 1),(-5, -4, -5)|`

= `hat"i"(- 10 + 4) - hat"j"(5 + 5) + hat"k"(4 + 10)`

= `-6hat"i" - 10hat"j" + 14hat"k"`

= `-2(3hat"i" + 5hat"j" - 7hat"k")`

Non-parametric vector equation:

`(vec"r" - vec"a")*(vec"b" xx vec"c") = vec0`

`[vec"r" - (6hat"i" - hat"j" + hat"k")]*(3hat"i" + 5hat"j" - 7hat"k") = vec0`

`vec"r"*(3hat"i" + 5hat"j" - 7hat"k")` = 18 – 5 – 7 = 6

`vec"r"*(3hat"i" + 5hat"j" - 7hat"k")` = 6

Cartesian equation:

3x + 5y – 7z = 6

3x + 5y – 7z – 6 = 0

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Different Forms of Equation of a Plane
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पाठ 6: Applications of Vector Algebra - Exercise 6.7 [पृष्ठ २६३]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
पाठ 6 Applications of Vector Algebra
Exercise 6.7 | Q 7 | पृष्ठ २६३

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