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Let ABC be a triangle whose circumcentre...

Let ABC be a triangle whose circumcentre is at P. If the position vectors of A, B, C and P are `vec(a) , vec(b) , vec(c ) and (vec(a) + vec(b) + vec(c ))/(4) `
respectively, then the position vector of the orthocentre of this triangle is

A

`- ( (veca + vecb + vec c)/(2))`

B

`veca + vecb + vec c `

C

`( (veca + vec b + vec c)/(2))`

D

`vec 0`

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The correct Answer is:
C
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DISHA PUBLICATION-VECTOR ALGEBRA-EXERCISE -2 : CONCEPT APPLICATOR
  1. Let ABC be a triangle whose circumcentre is at P. If the position vect...

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  2. The points D, E, F divide BC, CA and AB of the triangle ABC in the ra...

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  3. OABCDE is a regular hexagon of side 2 units in the XY-plane in the ...

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  4. The vectors bara (x) = cos xbar i + sin xbar j ,bar b(x)=xbar i + sin ...

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  5. The position vectors of the point A, B, C and D are 3hati-2hatj -hatk,...

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  6. Let x^2+3y^2=3 be the equation of an ellipse in the x-y plane. Aa n dB...

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  7. Let triangle PQR be a triangle. Let veca = vec(QR) , vecb = vec(RP) a...

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  8. If vec x and vec y are two non-collinear vectors and ABC is a triangle...

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  9. If vec u ,"" vec v , vec w are noncoplanar vectors and p, q are re...

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  10. Lelt two non collinear unit vectors hata and hatb form and acute angle...

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  11. A non-zero vecto veca is such tha its projections along vectors (hati ...

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  12. veca, vecb ,vec c are three vectors with magnitude |veca| = 4, |vecb|...

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  13. If the two adjacent sides of two rectangles are represented by vect...

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  14. OA, OB, OC are the sides of a rectangular parallelopiped whose diagona...

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  15. If the positive numbers a, b and c are the pth, qth and rth terms of G...

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

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  17. Let vecOB = hati + 2hatj + 2hatk " and" vecOA = 4hati + 2hatj + 2hatk ...

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  18. If a1 , a2 and a3 are three numbers satisfying a1^2 + a2^2 +a3^2 = 1 ,...

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  19. Let veca , vecb and vec c be non coplanar unit vectors equally incl...

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  20. Let veca , vecb, vec c be three non coplanar vectors , and let vecp ,...

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  21. Let veca= 2hati+hatj -2hatk and vecb=hati+hatj. If vec c is a vecto...

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