The vectors from origin to the points A and B are A→ $$=$$ $$3i^$$−$$6j^+2k^$$ and B→ $$=$$ $$2i^+j^$$−$$2k^$$ respectively. The area of the triangle OAB be

Question

The vectors from origin to the points A and B are A→ $$=$$ $$3i^$$−$$6j^+2k^$$   and  B→ $$=$$ $$2i^+j^$$−$$2k^$$ respectively. The area of the triangle OAB be

Infinity Learn · Accepted Answer

Given OA¯ $$=$$ a¯  $$=$$ $$3i^$$−$$6j^$$ $$+2k^$$   andOB¯ $$=$$ b¯  $$=$$ $$2i^+j^$$ −$$2k^$$   ∴  a→ ×b→ $$=$$ $$i^j^k^3$$−$$6221$$−$$2=$$ $$12$$−$$2i^$$ $$+4+6j^+3+12k^=$$ $$10i^$$ $$+10j^+15k^$$  ⇒ |a→×b→|$$=$$ $$102+102+152=$$ $$425$$ $$=$$ $$517Area$$ of ∆OAB $$=$$ $$=$$ $$12$$|a→ ×b→| $$=$$ $$5172$$ sq.unit.

The vectors from origin to the points A and B are $\vec{A} = 3 \hat{i} - 6 \hat{j} + 2 \hat{k} and \vec{B} = 2 \hat{i} + \hat{j} - 2 \hat{k}$ respectively. The area of the triangle OAB be

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The vectors from origin to the points A and B are A→ = 3i^−6j^+2k^ and B→ = 2i^+j^−2k^ respectively. The area of the triangle OAB be

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

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The vectors from origin to the points A and B are $\vec{A} = 3 \hat{i} - 6 \hat{j} + 2 \hat{k} and \vec{B} = 2 \hat{i} + \hat{j} - 2 \hat{k}$ respectively. The area of the triangle OAB be