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Dot-product of a vector with vectors 3ha...

Dot-product of a vector with vectors `3hati-5hatk,2hati+7hatj` and `hati+hatj+hatk` are respectively -1,6 and 5. find the vector.

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Dot product of a vector with vectors hati-hatj+hatk,2hatk+hatj+3hatk and hati+hatj+hatk are respectively 4,0 and 2. Find the vector.

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Find the angle between the vectors hati-2hatj+3hatk and 3hati - 2hatj + hatk

Show that the vectors 2hati-3hatj+4hatk and -4hati+6hatj-8hatk are collinear.

The position vectors of the vertices of /_\ABC are : 3hati-4hatj-4hatk,2hati-hatj+hatk and hati-3hatj-5hatk respectively. Find vec(AB),vec(BC) and vec(CA) .

If the vectors 2hati-hatj+hatk,hati+2hatj-3hatk and 3hati+ahatj+5hatk are coplanar, the prove that a=-4.

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MODERN PUBLICATION-VECTORS-Exercise
  1. Consider A(2,3,4),B(4,3,2) and C(5,2,-1) be any three points. Find the...

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  2. Consider A(2,3,4),B(4,3,2) and C(5,2,-1) be any three points. Find the...

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  3. Dot-product of a vector with vectors 3hati-5hatk,2hati+7hatj and hati+...

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  4. If hati+hatj+hatk, 2hati+5hatj, 3hati+2hatj-3hatk and hati-6hatj-hatk ...

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  5. If vecalpha=3hati+4hatj+5hatk and vecbeta=2hati+hatj-4hatk, then expre...

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  6. Prove that the perpendicular from the vertices to the opposite sides (...

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  7. Prove that in a right angled triangle the mid-point of the hypotenuse ...

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  8. If two medians of a triangle are equal, prove that the triangle is iso...

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  9. Which of the following statements are True or False : If the diagonals...

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  10. Prove that sum of squares of the diagonals of a parallelogram is equal...

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  11. In any DeltaABC prove by vectors that a^2=b^2+c^2-2 bc cos A.

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  12. In any DeltaABC prove by vectors that b^2=c^2+a^2-2 ca cos B.

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  13. In any triangle ABC, then by vectors, prove that : c^2=a^2+b^2-2ab cos...

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  14. Prove that, in any triangle ABC, cos B=(c^2+a^2-b^2)/(2ca).

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  15. With the help of vector method, prove that,cosA=(b^2+c^2-a^2)/(2bc)

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  16. In any triangle ABC, then by vectors, prove that : a=b cos C+c cos B.

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  17. Use vectors to prove that in triangleABC : b=c cos A+a cos C.

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  18. Using vector method prove that cos(A-B)=cosAcosB+sinAsinB

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  19. In any triangle ABC, show that AB^(2)+AC^(2)=2(AD^(2)+BD^(2)) wher...

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  20. Prove that any two edges in a regular tetrahedron are perpendicular.

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