A parallelogram is determined by the vectors a = [-2, 5] and b = [3, 2]. Determine the diagonals of the parallelogram.
The diagonals are obtained by the sum and difference of the two vectors:
a+b=<-2,5>+<3,2>=<1,7>
a-b=<-2,5>-<3,2>=<-5,3>
To determine the diagonals of a parallelogram given its vectors, you can use the vector addition and subtraction operations.
Step 1: Find the sum of the two given vectors.
You can find the sum of two vectors by adding their corresponding components together. Therefore, the sum of vectors a and b can be found as follows:
c = a + b = [-2, 5] + [3, 2] = [1, 7]
Step 2: Find the difference between the two given vectors.
You can find the difference between two vectors by subtracting their corresponding components. Therefore, the difference between vectors a and b can be found as follows:
d = a - b = [-2, 5] - [3, 2] = [-5, 3]
Step 3: The diagonals of the parallelogram are c and d.
So, the diagonals of the parallelogram determined by the vectors a = [-2, 5] and b = [3, 2] are c = [1, 7] and d = [-5, 3].