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Let ABC and PQR be any two triangles in ...

Let `ABC and PQR` be any two triangles in the same plane. Assume that the perpendiculars from the points `A, B, C` to the sides `QR, RP, PQ` respectively are concurrent. Using vector methods or otherwise,prove that the perpendiculars from `P, Q, R to BC, CA, AB` respectively are also concurrent.

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FIITJEE-VECTOR-SOLVED PROBLEMS (OBJECTIVE)
  1. Given that bara=3 hati+hatj+2 hatk and barb=hati-2 hatj-4 hatk are the...

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  2. A vector veca=(x,y,z) makes an obtuse angle with F-axis, and make equa...

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  3. Let ABC and PQR be any two triangles in the same plane. Assume that th...

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  4. Line L1 is parallel to vector vecalpha=-3 hat i+2 hat j+4 hat k and p...

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  5. IF OABC is a tetrahedron where O is the origin and A,B and C have resp...

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  6. Let bara,barb and barc be non coplanar unit vectors equally inclined t...

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  7. In a triangle PQR, S and T are points on QR and PR respectively, such ...

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  8. Let X be the midpoint of the side AB of triangle ABC. Let Y be the mid...

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  9. Let bara,barb,barc be unit vectors such that bara+barb+barc=bar0. Whic...

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  10. IF bara times barb = barc and barb times barc=bara then

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  11. barA,barB,barC are three vectors respectively given by 2hati+hatk,hati...

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  12. The number of distinct real values of lamda for which the vectors -lam...

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  13. If bara=i+j+k,bara.barb=1 and baraxxbarb=j-k, then : barb=

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  14. IF bara,barb,barc are unit vectors such that bara+barb+barc=0 then the...

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  15. If bara and barb are two unit vectors and theta is the angle between t...

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  16. If bara,barb,bar c are position vectors of the non- collinear points ...

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  17. Find a unit vector in XY plane, which makes an angle of 45^@ with the ...

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  18. OABC is a tetrahedron. The position vectors of A, B and C are i, i+j a...

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  19. Consider the points A (baro),B(3hati+f(t) hatj+hatk) and C(2hati+f'(t)...

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  20. If vectors ax hati+3hatj-5hatk and xhati+2hatj+2axhatk make an acute a...

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