The area of a parallelogram whose two adjacent sides are represen… - Vidyadip

MCQ

The area of a parallelogram whose two adjacent sides are represented by the vector $3i - k$ and $i + 2j$ is

A
$\frac{1}{2}\sqrt {17} $
B
$\frac{1}{2}\sqrt {14} $
✓
$\sqrt {41} $
D
$\frac{1}{2}\sqrt 7 $

✓

Answer

Correct option: C.

$\sqrt {41} $

c
(c) The area of parallelogram is given by

$ = |\overrightarrow {AB} \times \overrightarrow {AD} |$ $ = \frac{1}{2}|\overrightarrow {AC} \times \overrightarrow {BD} |$

Here we are given adjacent sides and so

$\overrightarrow {AB} \times \overrightarrow {AD} = \left| {\begin{array}{*{20}{c}}i&j&k\\3&0&{ - 1}\\1&2&0\end{array}} \right| = 2i - j + 6k$

Hence required area is $ = |2i - j + 6k| = \sqrt {41} .$

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