Misc 10 - Find unit vector parallel to parallelogram diagonal - Vector product - Area

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Misc 10 The two adjacent sides of a parallelogram are 2 4 + 5 and 2 3 Find the unit vector parallel to its diagonal. Also, find its area. Let and are adjacent side of a parallelogram, where = 2 4 + 5 = 2 3 Let diagonal be Hence, = + = (2 4 + 5 ) + (1 2 3 ) = (2 + 1) (4 + 2) + (5 3) = 3 6 + 2 Magnitude of = 3 2 + 6 2 + 2 2 = 9+36+4 = 49 = 7 Unit vector in direction of = 1 = 3 6 + 2 Area of parallelogram = So = 2 4 5 1 2 3 = 3 4 ( 2 5) 2 3 (1 5) + 2 2 ( 4 1) = (12 ( 10) ( 6 5) + ( 4 ( 4)) = (12 + 10) ( 11) + ( 4 + 4) = 22 + 11 + 0 = 22 + 11 So = 22 + 11 = 22 2 + 11 2 = 2 2 ( 11) 2 + 11 2 = 11 2 ( 2 2 +1) = 11 5 Hence, Area of parallelogram = =

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