Question

The area of a parallelogram whose one side is 3 i +j - k and one diagonal is 2 i + j - 2 k is​

Answer 1

Given:-

• one side of parallelogram  is 3 i +j - k .

• one diagonal is 2 i + j - 2 k .

To find:-

• Area of parallelogram.

Solution:-

We know,

Area of parallelogram :

✦ $\underline{\boxed{\pink{Area = \frac{1}{2} |a \times b| }}}$

Let us find a × b now :

$\mapsto a \times b = \left | \begin{array}{ccc}i&j&k\\3&1&-2\\1&-3&4\end{array}\right|\\\\\\ \\\implies -2i -14 j -10k\\\\\\\implies -2(i+7j+5k)$

Now,

➥ Area of the parallelogram = 1/2 |a×b|

                                                = 5√3.

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Answer 2

Given:-

one side of parallelogram  is 3 i +j - k .

one diagonal is 2 i + j - 2 k .

To find:-

Area of parallelogram.

Solution:-

We know,

Area of parallelogram :

✦ $\underline{\boxed{\pink{Area = \frac{1}{2} |a \times b| }}}$

Let us find a × b now :

$\mapsto a \times b = \left | \begin{array}{ccc}i&j&k\\3&1&-2\\1&-3&4\end{array}\right|\\\\\\ \\\implies -2i -14 j -10k\\\\\\\implies -2(i+7j+5k)$

Now,

➥ Area of the parallelogram = 1/2 |a×b|

                                                = 5√3.

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