Find the area of a parallelogram whose adjacent sides are given by the vectors $\to a = 3^i +^j + 4^k and^b =^i -^j +^k$

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Solution

$Given vectors : \to a = 3^i +^j + 4^k and \to b =^i -^j +^k$

$\to a \times \to b = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 3 & 1 & 4 1 & - 1 & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$

$\to a \times \to b =^i (1 \times 1 - (- 1) \times 4)$

$-^j (3 \times 1 - 1 \times 4)$

$+^k (3 \times (- 1) - 1 \times 1)$

$\to a \times \to b = 5^i +^j - 4^k$

$Magnitude of \to a \times \to b = \sqrt{5^{2} + 1^{2} + (- 4)^{2}}$

$| \to a \times \to b | = \sqrt{25 + 1 + 16} = \sqrt{42}$

$Area of parallelogram ABCD = | \to a \times \to b |$

$∴ Area of parallelogram ABCD = \sqrt{42}$

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Similar questions

\to a =^i -^j + 3^k

\to b = 2^i - 7^j +^k

\to a = 3^i +^j + 4^k

\to b =^i -^j +^k

3^i +^j - 2^k

^i - 3^j + 4^k

Find the area of the parallelogram whose adjacent sides are determined by the vectors $a =^i -^j + 3^k$ and $b = 2^i - 7^j +^k$

\to a = 2^i +^j +^k

^b =^i -^j -^k

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