The area of a parallelogram can be calculated using its diagonal vectors, specifically when given vectors $$\alpha = 2i + 6j - k$$ and $$\beta = 6i - 8j + 6k$$. The formula for the area is established as $$A = \frac{1}{2} \cdot \| \vec{\alpha} \times \vec{\beta} \|$$, where $$\times$$ denotes the cross product. This method allows for the determination of the area without needing the adjacent side vectors directly.
PREREQUISITESStudents and professionals in mathematics, physics, and engineering who need to calculate areas of geometric shapes using vector analysis.
Hint: If the diagonals of a parallelogram are known then you can find the sides. Figure out how.suvadip said:I can find the area of the parallelogram when two adjacent side vectors are given. But how to find the area of the parallelogram when diagonals of the parallelogram are given as
$$\alpha = 2i+6j-k$$ and $$\beta= 6i-8j+6k$$
suvadip said:I can find the area of the parallelogram when two adjacent side vectors are given. But how to find the area of the parallelogram when diagonals of the parallelogram are given as
$$\alpha = 2i+6j-k$$ and $$\beta= 6i-8j+6k$$