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D, E, F are the midpoints of the sides b...

D, E, F are the midpoints of the sides `bar(BC), bar(CA) " and " bar(AB)` respectively of the triangle ABC. If P is any point in the plane of the triangle, show that `vec(PA)+vec(PB)+vec(PC)=vec(PD)+vec(PE)+vec(PF)`.

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D,E,F are the midpoints of the sides bar(BC),bar(CA) and bar(AB) respectively of the triangle ABC. If P is any point in the plane of the traingle , show that bar(PA)+bar(PB)+bar(PC)= bar(PD)+bar(PE)+bar(PF) .

Let D, E, F are the midpoints of the sides bar(BC), bar(CA) " and " bar(AB) of the triangle ABC. Prove that vec(AD)+vec(BE)+vec(CF)=vec(0) .

If G be the centroid of the triangle ABC, then prove that vec(GA)+vec(GB)+vec(GC)=vec(0).

C is the midpoint of the line segment bar(AB) and O is any point outside AB, show that vec(OA)+vec(OB)=2vec(OC) .

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .

ABCD is a quadrilateral and E is the point of intersection of the lines joining the mid-points of opposite sides. If O be any point in the plane, then show that vec(OA)+vec(OB)+vec(OC)+vec(OD)=4vec(OE) .

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A(veca),B(vecb),C(vecc) are the vertices of the triangle ABC and R(vecr) is any point in the plane of triangle ABC , then vec r.(vecaxxvecb+vecbxxvecc+veccxxveca) is always equal to

CHHAYA PUBLICATION-VECTOR-EXERCISE - LONG ANSWER TYPE QUESTIONS
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  16. D, E, F are the midpoints of the sides bar(BC), bar(CA) " and " bar(AB...

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