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bara,barb,barc and bard are the position...

`bara,barb,barc and bard` are the position vectors of four coplanar points such that `(bara-bard).(barb-barc)=(barb-bard).(barc-bara)=0`. Show that the point `bard` represents the orthocentre of the triangle with `bara,barb and barc` as its vertices.

A

orthocentre

B

centroid

C

incentre

D

circumcentre

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The correct Answer is:
B
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AAKASH SERIES-DOT PRODUCT OF TWO VECTORS-EXERCISE - II
  1. If bara,barb,barc " are unit vectors, then " abs(bara-barb)^(2)+abs(ba...

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  2. If kbara = 3barb+2barc, bara=-2barb+5barc " and if " barb and barc hav...

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  3. bara,barb,barc and bard are the position vectors of four coplanar poin...

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  4. In a Delta ABC, bar(OA)= bara, bar(OB)=barb, bar(OC) = barc. if (bar...

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  5. ABC is an equitateral triangle of side 'a'. Then bar(AB).bar(BC)+bar...

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  6. In Delta ABC , angleABC=90^(@). If P and Q are points of trisection o...

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  7. A parallogram constructed on the vector bar(a) =3barp-barq and bar(b)...

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  8. The length of the projection of the vector (1,-2,-1) on the vector joi...

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  9. The magnitude of the projection of the vector bara=4bari-3barj+2bark o...

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  10. If barb=4bari+3barj and barc be two perpendicular vectors in xy-plane....

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  11. Let bara = 2bari -barj+bark , barb=bari+2barj-bark , barc=bari+barj-2b...

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  12. The triangle ABC is defined by the vertices A =(0,7,10), B = (-1,6,6) ...

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  13. In the Parallelogram ABCD, bar(AC)^(2)-bar(BD)^(2) =

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  14. The bot r bisecting plane of the line segment joining the points (3,1,...

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  15. The vector equation of the plane which contains the point (1,1,8) and ...

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  16. The perpendicular distance from origin to the plane passing through th...

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  17. Find the cartesian equation of the plane through the point A (2,-1,-4)...

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  18. The cartesian equation of the plane passing through (1,1,1) and contai...

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  19. The vector equation of the plane through the point (1,1,-1) and passin...

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  20. Let A = (bari-barj+3bark), B=(3bari+3barj+3bark) " be two points and "...

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