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Let hat(a), hat(b) and hat(c) be the non...

Let `hat(a), hat(b) and hat(c)` be the non-coplanar unit vectors. The angle between `hat(b) and hat(c)` be `alpha` and angled between `hat(c) and hat(a)` be `beta` and between `hat(a) and hat(b)` be `gamma`. If `A(hat(a)cosalpha, 0) , B(hat(b)cosbeta, 0) and C(hat(c)cosgamma, 0)`, then show that in `triangleABC`. `(|hat(a)times(hat(b)timeshat(c))|)/(sinA)=(|hat(b)times(hat(c)timeshat(a))|)/(sinB)=(|hat(c)times(hat(a)timeshat(b))|)/(sinC)`

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ARIHANT MATHS-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let hat(a), hat(b) and hat(c) be the non-coplanar unit vectors. The an...

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  2. Let O be the origin and let PQR be an arbitrary triangle. The point S ...

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  3. Let O be the origin and OX, OY, OZ be three unit vectors in the direct...

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  4. Let O be the origin, and O X , O Y , O Z be three unit vectors ...

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  5. Let a, b and c be three unit vectors such that atimes(btimesc)=(sqrt(3...

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  6. Let vec(a) , vec(b) and vec(c) be three non-zero vectors such that no ...

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  7. If a, b and c are unit vectors satisfying |a-b|^(2)+|b-c|^(2)+|c-a|^(2...

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  8. The vector(s) which is/are coplanar with vectors hat(i)+hat(j)+2hat(k)...

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  9. Let vec a =hat i+hat j+hat k,vec b=hat i -hat j+hat k and vec c =hat ...

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  10. Two adjacent sides of a parallelogram ABCD are given by vec(AB)=2hati+...

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  11. Let P, Q, R and S be the points on the plane with position vectors -2h...

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  12. If a and b are vectors in space given by a=(hat(i)-2hat(j))/(sqrt(5)) ...

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  13. If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb)*(...

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  14. The edges of a parallelopiped are of unit length and are parallel to ...

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  15. Lelt two non collinear unit vectors hata and hatb form and acute angle...

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  16. Let the vectors PQ, QR, RS, ST, TU and UP represent the sides of a reg...

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  17. The number of distinct real values of lambda, for which the vectors -l...

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  18. Let veca,vecb,vecc be unit vectors such that veca+vecb+vecc=vec0. Whic...

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  19. Let A be vector parallel to line of intersection of planes P1 and P2. ...

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  20. Let a=hat(i)+2hat(j)+hat(k), b=hat(i)-hat(j)+hat(k), c=hat(i)+hat(j)-h...

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  21. If vec a , vec b and vec c are three non-zero, non coplanar vecto...

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