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Prove that for any three vectors vec(a),...

Prove that for any three vectors `vec(a), vec(b)` and `vec(c), [vec(a) + vec(b) vec(b) + vec(c) vec(c) + vec(a)] = 2 [vec(a)vec(b)vec(c)]`

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Simplify [vec(a)-vec(b)vec(b)-vec(c)vec(c)-vec(a)] .

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Prove that [vec(a)vec(b)vec(c) + vec(d)] = [vec(a)vec(b)vec(c)] + [vec(a) vec(b)vec(d)] .

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ARIHANT PRAKASHAN-VECTORS -TOPIC TEST 2
  1. If vec(a),vec(b) and vec(c) are non - zero vectors, then vec(a)xxvec(b...

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  2. Find the angle between the vectors vec(a)=3hat(i)+2hat(j)-hat(k),vec(b...

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  3. Find the projection of the vector hat(i)-hat(j) on the vector hat(i)+h...

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  4. Find the projection of vec(b) + vec(c) on vec(a), where vec(a) = 2hat(...

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  5. Show that each of the given three vectors is a unit vector. 1/7(2hat...

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  6. Find |vec(x)|, if for a unit vector hat(a),(vec(x)-hat(a))*(vec(x)+hat...

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  7. If vec(a).vec(a) = 0 and vec(a).vec(b) = 0, then what can be concluded...

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  8. If vec(a), vec(b) and vec(c) are three vectors such that |vec(a)| = 5,...

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  9. Find the area of the triangle ABC with vertices A(1,2,4), B(3,1,-2) an...

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  10. Show that the vector area of the triangle whose vertices have position...

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  11. In a DeltaABC, prove by vector method b^(2)=a^(2)+c^(2)-2"ac "cosB.

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  12. Show that (vec(a)-vec(b))xx(vec(a)+vec(b))=2(vec(a)xxvec(b)).

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  13. Determine the area of parallelogram whose adjacent sides are the vecto...

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  14. Prove the following by vector method. The parallelogram whose diagonal...

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  15. Find the value of lamda so that the vectors hat(i)-hat(j)+hat(k),2hat(...

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  16. If the vectors a hat(i) + hat(j) + hat(k),hat(i) + b hat(j) + hat(k) a...

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  17. Prove that for any three vectors vec(a), vec(b) and vec(c), [vec(a) + ...

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

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  19. Find the value of hat(i).(hat(j) xx hat(k)) + hat(j).(hat(k) xx hat(i)...

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  20. If hat(a), hat(b), hat(c) are unit vectors and hat(a) xx (hat(b) xx ha...

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