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Prove that the lines joining the vertice...

Prove that the lines joining the vertices of a tetrahedron to the centroids of opposite faces are concurrent.

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i. Show that the lines joining the vertices of a tetrahedron to the centroids of opposite faces are concurrent. ii. Show that the joins of the midpoints of the opposite edges of a tetrahedron intersect and bisect each other.

The four lines drawing from the vertices of any tetrahedron to the centroid to the centroid of the opposite faces meet in a point whose distance from each vertex is 'k' times the distance from each vertex to the opposite face, where k is

Prove that the perpendicular let fall from the vertices of a triangle to the opposite sides are concurrent.

Prove that the volume of the tetrahedron and that formed by the centroids of the faces are in the ratio of 27:1.

Two coplanar triangles ABC and PQR re such that the lines drawn through the vertices of /_\ABC parallel to the sides of /_\PQR are concurrent. Prove that the lines drawn through the vertices of /_\PQR parallel to sides of /_\ABC are concurrent.

Prove that the line joining the orthocentre to the centroid of a triangle formed by the focal chord of a parabola and tangents drawn at its extremities is parallel to the axis of the parabola.

Prove that the medians of a triangle are concurrent.

Prove that the altitudes of a triangle are concurrent.

Show that the line joining one vertex of a parallelogram to the mid-point of an opposite side trisects the diagonal and is trisected thereat.

In a right triangle,Prove that the line-segment joining the mid-point of the hypotenuse to the opposite vertex is half the hypotenuse

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. Check whether the three vectors 2 hat i+2 hat j+3 hat k ,-3 hat i+3...

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  2. The midpoint of two opposite sides of a quadrilateral and the midpo...

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  3. Prove that the lines joining the vertices of a tetrahedron to the ce...

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  4. Find the angle of vector vec a = 6 hat i + 2 hat j - 3 hat k with x -...

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  5. If the vectors vecalpha=a hat i+a hat j+c hat k , vecbeta= hat i+ hat...

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  6. The points with position vectors 60 i+3j ,40 i-8j ,a i-52 j are col...

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  7. Let alpha, beta and gamma be distinct real numbers. The points whose ...

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  8. Let vec a= vec i- vec k , vec b=x vec i+ vec j+(1-x) vec k and vec c...

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  9. In the DeltaOAB,M is the mid-point of AB,C is a point on OM, such that...

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  10. If vec a , vec b are two non-collinear vectors, prove that the poi...

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  11. If vec a= hat i+ hat j+ hat k , vec b=4 hat i+3 hat j+4 hat k and ve...

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  12. The number of distinct real values of lambda , for which the vectors...

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  13. If vec A O+ vec O B= vec B O+ vec O C , then A ,B and C are (where O...

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  14. Find a vector magnitude 5 units, and parallel to the resultant of t...

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  15. Show that the points A(1,-2,-8),B(5,0,-2)a n dC(11,3,7) are collinear,...

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  16. The position vectors of Pa n dQ are 5 hat i+4 hat j+a hat k and - hat ...

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  17. Given three points are A(-3,-2,0),B(3,-3,1)a n dC(5,0,2)dot Then find ...

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  18. Let A B C D be a p[arallelogram whose diagonals intersect at P and ...

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  19. If A B C D is quadrilateral and Ea n dF are the mid-points of A Ca n d...

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  20. If A B C D is a rhombus whose diagonals cut at the origin O , then p...

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