Example 25 - Find area of a parallelogram whose a = 3i + j + 4k - Vector product - Area

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Example 25 Find the area of a parallelogram whose adjacent sides are given by the vectors a = 3 + + 4 and b = + k a = 3 + 1 + 4 b = 1 1 + 1 k Area of parallelogram ABCD = = 3 1 4 1 1 1 = (1 1 ( 1) 4) (3 1 1 4) + (3 1 1 1) = (1 (-4)) j (3 4) + ( 3 1) = (1 + 4) j ( 1) + ( 4) = 5 + 4 Magnitude of = 52+ 1 2 + 4 2 = 25+1+16 = 42 Area of parallelogram ABCD = = 42 Therefore, the required area is .

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