Find the area of the parallelogram whose diagonals are a-2-3k- and b-3-2-k-

Area of parallelogram = 1 2 | d⃗ ⃗_⃗ ⃗1⃗×d⃗ ⃗_⃗ ⃗2⃗ #160; | = 1 2 | î #160; amp; ĵ #160; amp; k̂ #160; 1 amp; 2 amp; 3 ...

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Addition of vectors

Find the area...

Question

Find the area of the parallelogram whose diagonals are $\to a =^i - 2^j + 3^k$ and $\to b = 3^i - 2^j +^k$ .

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Solution

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\to a \times \to b

\to a =^i + 2^j + 3^k

\to b = 3^i + 2^j +^k

\to a = 3^i + 4^j + 3^k

\to b = 3^i - 2^j +^k .

\to a

\to b

\to a = 3^i - 2^j +^k

\to b =^i - 2^j - 3^k

A parallelogram has diagonals expressed as $\to A = 5^i - 4^j + 3^k$ and $\to B = 3^i + 2^j -^k$ . Area of parallelogram is:

\to a = 2^i +^j + 3^k

\to b = 3^i + 2^j +^k

\to c =^i -^j - 4^k

\to d =^i + 2^j -^k

(\to a \times \to b) \times (\to c \times \to d) =

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