Q. 315.0( 1 Vote )

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

Answer :

Let ABCD be a parallelogram with sides AB and AC given.


We have and



We need to find unit vector parallel to diagonal.


From the triangle law of vector addition, we have






Let the unit vector in the direction of be.


We know unit vector in the direction of a vector is given by .



Recall the magnitude of the vector is



Now, we find.





So, we have



Thus, the required unit vector that is parallel to diaonal is.


Now, we have to find the area of parallelogram ABCD.


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



Here, we have (a1, a2, a3) = (2, –4, 5) and (b1, b2, b3) = (1, –2, –3)






Recall the magnitude of the vector is



Now, we find.





Thus, area of the parallelogram is square units.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Lecture on Product of DeterminantsLecture on Product of DeterminantsLecture on Product of Determinants58 mins
When does a Maxima or Minima occur?When does a Maxima or Minima occur?When does a Maxima or Minima occur?48 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :