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
\(\displaystyle \alpha = 2i+6j-k\) and \(\displaystyle \beta= 6i-8j+6k\)
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
\(\displaystyle \alpha = 2i+6j-k\) and \(\displaystyle \beta= 6i-8j+6k\)
The formula for finding the area of a parallelogram when diagonal vectors are given is: Area = magnitude of vector 1 * magnitude of vector 2 * sine of the angle between the two vectors.
The magnitude of a vector can be found using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squares of its components.
No, the angle between diagonal vectors must be acute (less than 90 degrees) for the area formula to be accurate.
No, the area of a parallelogram cannot be negative as it represents a physical measurement and cannot have a negative value.
Yes, this formula can be used to find the area of any parallelogram as long as the given vectors are the diagonals of the parallelogram and the angle between them is acute.