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If veca=-2hati+3hatj+5hatk,vecb=hati+2ha...

If `veca=-2hati+3hatj+5hatk,vecb=hati+2hatj+3hatkandvecc=7hati-hatk` are position vectors of three points A, B, C respectively, prove that A, B, C are collinear.

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MODERN PUBLICATION-VECTORS-Exercise
  1. Show that the following points are collinear : A(-2,1),B(-5,-1),C(1,3)...

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  2. Show that the following points are collinear : A(1,2,7),B(2,6,3),C(3,1...

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  3. If veca=-2hati+3hatj+5hatk,vecb=hati+2hatj+3hatkandvecc=7hati-hatk are...

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  4. Show that the following vectors are coplanar : hati-hatj+hatk,6hati-ha...

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  5. Show that the following vectors are coplanar : 3hati-2hatj+4hatk,6hati...

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  6. Show that the following vectors are coplanar : 2hati-hatj+hatk,hati-3h...

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  7. Show that the points A(3,-2,1),B(1,-3,5),C(2,1,-4) do not form a right...

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  8. If the position vectors of the vertices of a triangle are : vecA=hati+...

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  9. If veca = hati + hatj+hatk, vecb = 2hati-hatj+3hatk and vecc = hati-2h...

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  10. Show that the four points A,B,C,D with position vectors veca*vecb*vecc...

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  11. Show that the four points P,Q,R,S with position vectors vecp,vecq,vecr...

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  12. Prove that the necessary and sufficient condition for three vectors ve...

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  13. If veca,vecb,vecc,vecd respectively, are position vectors representing...

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  14. If Q is the point of intersection of the medians of a triangle ABC, pr...

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  15. G is the centroid of a triangle ABC, show that : vec(GA)+vec(GB)+vec(G...

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  16. Let veca,vecb,vecc,vecd be the position vectors of the four distinct p...

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  17. Show that the line joining any vertex of a parallelogram to the mid-po...

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  18. Prove that the figure formed by joining the mid-points of the pairs of...

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  19. Show that if P,A,B are any three points, then lambda vec(PA)+mu vec(PB...

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  20. Obtain the dot product of the vectors : veca=veci-hatj+hatk and vecb=v...

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