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If the points A,B,C and D have position ...

If the points `A,B,C and D` have position vectors `bara,2bara+barb,4bara+2barb and 5 bara+4barb` respectively, then three collinear points are

A

`A,B,D`

B

`A,B,C`

C

`B,C,D`

D

`A,C,D`

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A
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Show that vectors |barb|bara+|bara|barb and |barb||bara-|bara|b are orthogonal.

IF OABC is a tetrahedron where O is the origin and A,B and C have respective positions vectors as bara,barb and barc then prove that the circumcentre of the tetrahedron is ((bara)^2(barb times barc)+(barb)^2 (barc times bara)+(barc)^2 (bara times barb))/(2[bara barb barc])

If bara and barb are unit vectors such that bara + 2barb and 5bara- 4barb are perpendicular to each other, then the angle between bara and barb is

TARGET PUBLICATION-VECTORS-Critical Thinking
  1. Three points whose position vectors are bara+barb,bara-barb and bara+k...

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  2. If bara,barb and barc be there non-zero vectors, no two of which are c...

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  3. If the points A,B,C and D have position vectors bara,2bara+barb,4bara+...

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  4. If bara=2barp+3barq-barr,barb=barp-2barq+2barr and barc=-2barp+barq-2b...

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  5. If bara+barb+barc=lambdabard and barb+barc+bard=mubara and bara,barb,b...

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  6. A and B are two points. The position vector of A is 6b-2a. A point P ...

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  7. If bar(a),bar(b),bar(c)are the position vectors of the points A, B, C ...

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  8. If bar(OA)=overset(^)i+3overset(^)j-2overset(^)k and bar(OB)=3overset(...

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  9. bara,barb are position vectors of points A and B. If P divides AB in t...

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  10. If 2bara+barb=3barc, then A divides BC in the ratio

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  11. In DeltaABC, P is the mid point of BC,Q divides CA internally in the r...

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  12. If overset(to)(a) =hat(i) - hat(k) , overset(to)(b) = x hat(i) + ...

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  13. If the points (1,1,2),(2,1,p),(1,0,3) and (2,2,0) are co-planar then ...

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  14. If the points A, B, C and D with position vectors overset(^)i+overset(...

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  15. If aoverset(^)i+overset(^)j+overset(^)k,overset(^)i-boverset(^)j+overs...

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  16. If the given vectors (-bc,b^2+bc,c^2+bc)(a^2+ac,-ac,c^2+ac) and (a^2+a...

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  17. If bara,barb,barc are non-zero, non collinear vectors, then the vector...

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  18. Given vectors bara,barb,barc such that bara.(barbxxbarc)=lambda!=0 the...

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  19. For any three vectors bara,barb and barc,(bara-barb)[(barb+barc)xx(bar...

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  20. If bara,barb and barc are three non-coplanar vectors, then : (bara + b...

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