Question

plz solve it........ ​

Answer 1

GIVEN :–

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• $\bf \overrightarrow{a} = 3 \hat{i} - \hat{j} + 2 \hat{k}$ and $\bf \overrightarrow{b} = \hat{i}+ 4 \hat{j} -6 \hat{k}$ are adjacent sides of parallelogram .

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TO FIND :–

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• Area of parallelogram = ?

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SOLUTION :–

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• We know that area of parallelogram is –

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$\bf \implies \large{ \boxed{ \bf Area =| \overrightarrow{a} \times \overrightarrow{b}|}}$

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$\bf \implies Area =|(3 \hat{i} - \hat{j} + 2 \hat{k} )\times ( \hat{i}+ 4 \hat{j} -6 \hat{k})|$

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$\bf \implies Area = \left|\begin{array}{ccc}\bf\hat{i} & \bf\hat{j}& \bf\hat{k} \\ \\\bf3& \bf - 1& \bf2 \\ \\\bf1& \bf 4& \bf - 6\end{array}\right|$

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$\bf \implies Area =|\hat{i} \{ ( - 1)( - 6) - (4)(2)\} -\hat{j} \{ (3)( - 6) - (4)(2)\} + \hat{k} \{ ( 4)(3) - (1)( - 1)\}|$

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$\bf \implies Area =|\hat{i} \{6 - 8\} -\hat{j} \{ - 18- 8\} + \hat{k} \{12 -( - 1)\}|$

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$\bf \implies Area =|\hat{i} \{ - 2\} -\hat{j} \{ -26\} + \hat{k} \{12 + 1\}|$

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$\bf \implies Area = |- 2\hat{i} + 26\hat{j}+13 \hat{k}|$

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$\bf \implies Area = \sqrt{ {( - 2)}^{2} + {(26)}^{2} + {(13)}^{2} }$

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$\bf \implies Area = \sqrt{4+ 676+169}$

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$\bf \implies Area = \sqrt{849} \:\:sq.\:\: units$

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$\bf \implies {\boxed{ \bf Area = 29.14 \:\:sq.\:\: units}}$

Answer 2

GIVEN :–

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• $\bf \overrightarrow{a} = 3 \hat{i} - \hat{j} + 2 \hat{k}$ and $\bf \overrightarrow{b} = \hat{i}+ 4 \hat{j} -6 \hat{k}$ are adjacent sides of parallelogram .

ㅤ

TO FIND :–

ㅤ

• Area of parallelogram = ?

ㅤ

SOLUTION :–

ㅤ

• We know that area of parallelogram is –

ㅤ

$\bf \implies \large{ \boxed{ \bf Area =| \overrightarrow{a} \times \overrightarrow{b}|}}$

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$\bf \implies Area =|(3 \hat{i} - \hat{j} + 2 \hat{k} )\times ( \hat{i}+ 4 \hat{j} -6 \hat{k})|$

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$\bf \implies Area = \left|\begin{array}{ccc}\bf\hat{i} & \bf\hat{j}& \bf\hat{k} \\ \\\bf3& \bf - 1& \bf2 \\ \\\bf1& \bf 4& \bf - 6\end{array}\right|$

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$\bf \implies Area =|\hat{i} \{ ( - 1)( - 6) - (4)(2)\} -\hat{j} \{ (3)( - 6) - (4)(2)\} + \hat{k} \{ ( 4)(3) - (1)( - 1)\}|$

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$\bf \implies Area =|\hat{i} \{6 - 8\} -\hat{j} \{ - 18- 8\} + \hat{k} \{12 -( - 1)\}|$

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$\bf \implies Area =|\hat{i} \{ - 2\} -\hat{j} \{ -26\} + \hat{k} \{12 + 1\}|$

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$\bf \implies Area = |- 2\hat{i} + 26\hat{j}+13 \hat{k}|$

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$\bf \implies Area = \sqrt{ {( - 2)}^{2} + {(26)}^{2} + {(13)}^{2} }$

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$\bf \implies Area = \sqrt{4+ 676+169}$

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$\bf \implies Area = \sqrt{849} \:\:sq.\:\: units$

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$\bf \implies {\boxed{ \bf Area = 29.14 \:\:sq.\:\: units}}$