First slide

Vectors

Question

The diagonals of a parallelogram are 2 i and 2 j. The area of parallelogram is

Moderate

A

0 .5 unit
B

1 unit
C

2 unit
D

4 unit

Solution

Let the sides of the parallelogram be A and B. Then
A+B=2i and A-B=2j
$∴$ A = i+j and B = i -j
Now area of parallelogram $= | A \times B |$
$\begin{array}{l} = | (i + j) \times (i - j) | \\ = | (- i \times j + j \times i) | = | - k - k | \\ = 2 units \end{array}$

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