Solve 44 The two adjacent sides of a parallelogram are 2i^ - 4j^ - 5k^ and 2i^ - Maths - Vector Algebra

Question

Solve

44 The two adjacent
sides of a parallelogram are 2 i ^   -   4 j ^   -
  5 k ^   a n d   2 i ^   +   2 j ^  
+   3 k ^ Find the two unit vectors parallel to its diagonals
Using the diagonal vectors, find the area of the parallelogram

Neha Sethi · Accepted Answer

Dear student
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5aaa478970103%20png">
Note:P→=a→+b→=2i-4j-5k+2i+2j+3k=4i-2j-2kand P'→=b→-a→=2i+2j+3k-2i+4j+5k=6j+8kNow, P→×P'→=ijk4-2-2068=i-16+12-j32+k24=-4i-32j+24kNow, P→×P'→=-42+-322+242=16+1024+576=1616=4101 
Regards

Solve 44. The two adjacent sides of a parallelogram are 2 i ^ - 4 j ^ - 5 k ^ a n d 2 i ^ + 2 j ^ + 3 k ^ . Find the two unit vectors parallel to its diagonals. Using the diagonal vectors, find the area of the parallelogram.

Solve

44. The two adjacent sides of a parallelogram are $2 \hat{i} - 4 \hat{j} - 5 \hat{k} a n d 2 \hat{i} + 2 \hat{j} + 3 \hat{k}$ . Find the two unit vectors parallel to its diagonals. Using the diagonal vectors, find the area of the parallelogram.