The area of the parallelogram represented by the vectors A - 2 - - 3- and B - - - 4- as its sides is

Area of parallelogram= |A×B| nbsp; Here A×B = (2 î + 3 ĵ) × (î + 4 ĵ) ⇒ nbsp;A×B = 8 k̂ 3 k̂ ⇒ nbsp; A×B= 5 k̂ ∴Magnitude of area = |A×B| = 5 Units ...

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Standard XII

Mathematics

Dot Product of Two Vectors

The area of t...

Question

The area of the parallelogram represented by the vectors $\to A = 2^i + 3^j$ and $\to B =^i + 4^j$ as its sides is

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Solution

$Area of parallelogram = | \to A \times \to B |$
Here $\to A \times \to B = (2^i + 3^j) \times (^i + 4^j)$
$\Rightarrow \to A \times \to B = 8^k - 3^k$
$\Rightarrow \to A \times \to B = 5^k$
$∴ Magnitude of area = | \to A \times \to B | = 5 Units$

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The area of the parallelogram represented by the vectors →A=2^i+3^j and →B=^i+4^j as its sides is

Area of parallelogram=|→A×→B| Here →A×→B=(2^i+3^j)×(^i+4^j) ⇒→A×→B=8^k−3^k ⇒→A×→B=5^k ∴Magnitude of area=|→A×→B|=5 Units

The area of the parallelogram represented by the vectors $\to A = 2^i + 3^j$ and $\to B =^i + 4^j$ as its sides is

$Area of parallelogram = | \to A \times \to B |$
Here $\to A \times \to B = (2^i + 3^j) \times (^i + 4^j)$
$\Rightarrow \to A \times \to B = 8^k - 3^k$
$\Rightarrow \to A \times \to B = 5^k$
$∴ Magnitude of area = | \to A \times \to B | = 5 Units$