Question

The area of a parellelogram whose sides are represented by vectors j+3k and i+2j-k is ?

Answer 1

Explanation:

Sides of parallelogram -

1.i^ + 3k

2.i^ + 2j^ - k^

To find :

Area of the parallelogram.

Solution :

We are given vectors which represent two adjacent sides of a parallelogram.

To find the area, we take the cross product of the given vectors.

The magnitude of the cross product will give us the area of the parallelogram.

Let C be a vector which is the cross product of the given two vectors.

∴ Vector C = (i^ + 3k^) x (i^ +2j^ - k^)

\begin{gathered}Vector C = \left[\begin{array}{ccc}i^&j^&k^\\1&0&3\\1&2&-1\end{array}\right]\end{gathered}

= -6i^ +4j^ + 2k^

Now, Area = Magnitude of vector C

= \sqrt{36 + 16 + 4}

36+16+4

Area = \sqrt{56}Area=

56

Answer : The area of the parallelogram will be \sqrt{56}

56

sq. units