Question

Find the area of a parallelogram formed by vectors
Å=3icap+2jcap, B=-3icap+7jcap​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer:-}}}}$

$\mathfrak{\large{\underline{\underline{Given:-}}}}$

→

A = 3 I + 2 j

→

B = 3 I + 7 j

$\mathfrak{\large{\underline{\underline{</strong><strong>T</strong><strong>o</strong><strong> </strong><strong>find</strong><strong>:-}}}}$

Area of parallelogram= ?

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We know, that area of parallelogram = ★ $\boxed{\sf{ </strong><strong>A</strong><strong> </strong><strong>×</strong><strong> </strong><strong>B</strong><strong>}}$

area of parallelogram = $\bold{</strong><strong>(3i + 2j) \: \times \: ( - 3i \: + 7j)</strong><strong> }$

★ $\boxed{\sf{</strong><strong>i</strong><strong> </strong><strong>×</strong><strong> </strong><strong>i</strong><strong> </strong><strong>=</strong><strong> </strong><strong>0</strong><strong>}}$

★ $\boxed{\sf{</strong><strong>i</strong><strong> </strong><strong>×</strong><strong> </strong><strong>j</strong><strong> </strong><strong>=</strong><strong> </strong><strong>0</strong><strong>}}$

★ $\boxed{\sf{ </strong><strong>I</strong><strong> </strong><strong>×</strong><strong> </strong><strong>j</strong><strong> </strong><strong>=</strong><strong> </strong><strong>k</strong><strong>}}$

★ $\boxed{\sf{ </strong><strong>j</strong><strong> </strong><strong>×</strong><strong> </strong><strong>I</strong><strong> </strong><strong>=</strong><strong> </strong><strong>-</strong><strong>k</strong><strong>}}$

= $\bold{</strong><strong>3i \times ( - 3i) + 3i \times 7j + 2j \times ( - 3i) + 2j \times 7j</strong><strong>}$

= $\bold{ </strong><strong>0 + 21k - 6</strong><strong>(</strong><strong>-</strong><strong>k</strong><strong>)</strong><strong> </strong><strong>+ 0</strong><strong>}$

= $\bold{</strong><strong>2</strong><strong>7</strong><strong> </strong><strong>k</strong><strong>}$

hence, area of parallelogram is 27 sq. units

Answer 2

Answer:

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