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

D, E, F are the midpoints of the sides BC, CA and AB respectively of `triangleABC` and O is any point in the plane of `triangleABC`. Show that (1)` bar(AD)+bar(BE)+bar(CF)=bar(0)`

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NAVNEET PUBLICATION - MAHARASHTRA BOARD-VECTORS-Examples for Practics
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  6. Show that if bar(AB)=bar(DC), then the figure ABCD is a parallelogram.

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  7. If G is the centroid of triangleABC and O is any point in the plane of...

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  8. Find [bar(a)bar(b)bar(c)] where : (1) bar(a)=2hat(i)+hat(j)-hat(k),b...

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  9. If bar(a)=hat(i)+hat(j)+hat(k),bar(b)=2hat(i)+qhat(j)+hat(k),hat(c)=ha...

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  10. Show that the vectors hat(i)-hat(j)-6hat(k),hat(i)-3hat(j)+4hat(k)and2...

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  11. Find the volume of the parallelopiped whose coterminus edges are : (...

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  12. Find lamda, if the vectors bar(a)=hat(i)+hat(j)+hat(k),bar(b)=hat(i)-h...

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  13. If bar(a),bar(b),bar(c) are any three vectors, prove that (1) [bar(a)...

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  14. Find the volume of the parallelopiped with segments AB, AC and AD as c...

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  15. Find the volume of the tetrahedron whose vertices are A(3,7,4),B(5,-2,...

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  16. Find the volume tetrahedron whose coterminus edges are 7hat(i)+hat(k),...

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  17. Show that the following sets of points are coplanar : (1) (3,9,4),(0...

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  19. If the origin and the points P(2,3,4), Q(1,2,3) and R(x,y,z) are copla...

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  20. If bar(u)=bar(i)-2bar(j)+bar(k),bar(v)=3bar(i)+bar(k)andbar(w)=bar(j)-...

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