To find the lengths of the diagonals of the parallelogram with adjacent sides represented by the vectors
=+− and
=2−3+, we need to determine the diagonals using the vector addition and subtraction.
The diagonals of the parallelogram can be given by
+ and
−.
First, let's compute
+ :
Combining like terms, we get:
Now, let's find the magnitude of this vector:
Next, let's compute
− :
Combining like terms, we get:
Now, let's find the magnitude of this vector:
Thus, the lengths of the diagonals of the parallelogram are
√13 and
√21.
The correct option is:
Option D
√21,√13