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If `bar(a), bar(b), bar(c )` respresents the vertices A, B, and C respectively of `DeltaABC` then prove that `|(bar(a) xx bar(b)) + (bar(b) xx bar(c ))+ (bar(c ) xx bar(a))|` is twice the area of `DeltaABC`.

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AAKASH SERIES-VECTOR (CROSS) PRODUCT OF TWO VECTORS-Exercise-3.1 ( Short Answer Questions)
  1. Find a vector of magnitude and perpendicular to both the vectors vec(a...

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  2. Find a vector of length sqrt6 and perpendicular to both vec(a)= 2vec(i...

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  3. Find the unit vector perpendicular to the plane passing through the po...

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  4. Find a unit vector perpendicular to the plane determined by the points...

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  5. Let bar(a)= bar(i) + 2bar(j) + 3bar(k), bar(b)= - bar(i) + 2bar(j) + 3...

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  6. If vec(a)= 4vec(i) + 5vec(j)- vec(k), vec(b)= vec(i)- 4vec(j) + 5vec(k...

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  7. If bar(a), bar(b), bar(c ) respresents the vertices A, B, and C respe...

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  8. If vec(a) = 2vec(i) + 3vec(j) + 4vec(k), vec(b)= vec(i) + vec(j)- vec(...

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  9. If vec(a) = 7vec(i) -2vec(j) + 3vec(k), vec(b)= 2vec(i) + 8vec(k), vec...

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  10. vec(a)= 2vec(i) + vec(j) -vec(k), vec(b)= -vec(i) + 2vec(j)- 4vec(k) a...

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  11. vec(a)= 3vec(i)- vec(j) + 2vec(k), vec(b)= -vec(i) + 3vec(j) + 2vec(k)...

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  12. If vec(a)-vec(i)-2vec(j)-3vec(k), vec(b)=2vec(i)+vec(j)-vec(k) and vec...

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  13. If vec(a)= vec(i) + vec(j)+ vec(k), vec(c )= vec(j)- vec(k), then find...

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  14. If vec(a).vec(b) = vec(a).vec(c ) and vec(a) xx vec(b)= vec(a) xx vec(...

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  15. If bar(a) xx bar(b) = bar(b) xx bar(c ) != 0, then show that bar(a) + ...

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  16. If the vectors vec(a), vec(b), vec(c ) form the sides vec(BC), vec(CA)...

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  17. If vec(a) xx vec(b) = vec(c ) xx vec(d) and vec(a) xx vec(c )= vec(b) ...

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  18. Let vec(a)= 2vec(i) + vec(j)-2vec(k), vec(b)= vec(i) + vec(j) " if " ...

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  19. Let vec(a), vec(b), vec(c ) be such that vec(c ) ne vec(0), vec(a) xx ...

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  20. If |vec(a)|= |vec(b)|=5, (vec(a), vec(b))= 45^(@), then find the area ...

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