Question

Find the area of parallelogram whose diagonal are represented by (3i+j+k) and (i-j-k)​

Answer 1

Given:-

Diagonals of the parallelogram are:

a = (3i+j+k),

b = (i-j-k)

To find:-

Area of parallelogram

Solution:-

we know that,

Simply, Area of parallelogram is the Half of the cross product of the diagonals of it.

Or,

The area of parallelogram formula using diagonals in vector form is, area = 1/2 |(→d1 d 1 → × →d2 d 2 → )|,

where →d1 d 1 → and →d2 d 2 → are diagonal vectors.

we can say that,

Area of parallelogram = 1/2 ∣a×b∣

Here,

a=3i+j−2k,

b=i−3j+4k

Thus,

a×b = −2i−14j−10k

= −2(i+7j+5k)

Now, area of parallelogram = 1/2 |(→d1 d 1 → × →d2 d 2 → )|,

=5√3.

Hence the area of parallelogram is 5√3.