Q30 of 93 Page 25

If are three vectors, find the area of the parallelogram having diagonals and

Given, and


We need to find area of the parallelogram with vectors and as diagonals.








Recall the area of the parallelogram whose diagonals are given by the two vectors and is where



Here, we have (a1, a2, a3) = (1, –3, 2) and (b1, b2, b3) = (–1, 2, 0)






Recall the magnitude of the vector is



Now, we find.






Thus, area of the parallelogram is square units.


More from this chapter

All 93 →
28

Find a unit vector perpendicular to each of the vectors and where and

29

Using vectors, find the area of the triangle with vertices A(2, 3, 5), B(3, 5, 8) and C(2, 7, 8).

 31

The two adjacent sides of a parallelogram are and Find the unit vector parallel to one of its diagonals. Also, find its area.

 32

If either or then Is the converse true? Justify your answer with an example.