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Last updated at Dec. 5, 2018 by Teachoo

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Area of parallelogram whose diagonals are given Let us consider a parallelogram ABCD Here, π β + π β = (π_1 ) β and π β + (βπ β) = (π_2 ) β π β β π β = (π_2 ) β Letβs find (π_1 ) β Γ (π_2 ) β (π_1 ) β Γ (π_2 ) β = (π β + π β) Γ (π β β π β) = π β Γ (π β β π β) + π β Γ (π β β π β) = π β Γ π β β π β Γ π β + π β Γ π β β π β Γ π β Since π β Γ π β = 0 = π β Γ π β β 0 + 0 β π β Γ π β = π β Γ π β β π β Γ π β Since π β Γ π β = β (π β Γ π β) = π β Γ π β β (β (π β Γ π β)) = (π β Γ π β) + (π β Γ π β) = 2 (π β Γ π β) Therefore, (π_1 ) β Γ (π_2 ) β = 2 (π β Γ π β) Now, we know that Area of parallelogram = |π β" Γ " π β | Writing in terms of diagonals Area of parallelogram = π/π |(π _π ) βΓ(π _π ) β |

Chapter 10 Class 12 Vector Algebra

Concept wise

- Scalar or vector
- Graphical displacement
- Type of vector
- Multiplication of a vector by a scalar
- Equal vectors
- Unit vector
- Direction cosines and ratios
- Addition(resultant) of vectors
- Joining two points
- Section formula
- Right Angled triangle
- Collinearity Of two vectors
- Collinearity of 3 points or 3 position vectors
- Scalar product - Defination
- Scalar product - Projection
- Scalar product - Solving
- Vector product - Defination
- Vector product - Area
- Vector product - Solving

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.