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Using properties of scalar triple produc...

Using properties of scalar triple product, prove that `[(bar(a) + bar(b),bar(b) + bar(c), bar(c) + bar(a))] = 2 [(bar(a),bar(b),bar(c))]`

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NAVNEET PUBLICATION - MAHARASHTRA BOARD-QUESTION BANK 2021-VECTOR AND THREE DIMENSIONAL GEOMETRY
  1. Find the centroid of tetrahedron with vertices K(5, -7, 0), L(1, 5, 3)...

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  2. If a line has the direction ratios 4, -12, 18, then its direction cos...

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  3. Show that the points A(2, -1, 0) B(-3, 0, 4), C(-1, -1, 4) and D(0, -5...

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  4. Using properties of scalar triple product, prove that [(bar(a) + bar(b...

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  5. The direction ratios of AB are -2,2,1. If A -= (4,1,5) and l(AB) = 6 u...

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  6. If G(a,2,-1) is the centroid of the triangle with vertices P(1,3,2),Q(...

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  7. If G(r, (-4)/(3), (1)/(3)) is centroid of the triangle having vertices...

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  8. Prove that an angle inscribed in a semi-circle is a right angle usi...

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  9. Prove using vectors: Medians of a triangle are concurrent.

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  10. Show that the perpendicular bisectors of the sides of a triangle are c...

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  11. Express -hat(i)-3hat(j)+4hat(k) as the linear combination of the vecto...

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  12. If Q be the foot of perpendicular from P(2, 4, 3) on the line joining ...

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  13. Prove that the internal bisectors of the angles of a triangle are conc...

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  14. Using vector method, find the incenter of the triangle whose vertices ...

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  15. The angle between the lines whose direction cosines l, m, n satisfy t...

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  16. If A (bara) and B (barb) are any two points in the space and R(b...

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  17. D,E divide sides BC and CA of a triangle ABC in the ratio 2:3 respecti...

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  18. D,E divide sides BC and CA of a triangle ABC in the ratio 2:3 respecti...

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  19. Find the value of a tetrahedrn whose vertices are A(-1,2,3),B(3,-2,1),...

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  20. If four points A (overset(-)a), B(overset(-)b), C (overset(-)c) & D(o...

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