Q9 of 177 Page 23

Find the vector from the origin O to the centroid of the triangle whose vertices are (1, -1, 2), (2, 1, 3) and (-1, 2, -1).

Centeroid of the triangle with Vertices (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) is given by,



In vector algebra, ‘x’ consider as a coefficient of and ‘y’ as a coefficient of and ‘z’ as a coefficient of


So the position vector of the centroid,




So the location of the centroid is


And the vector is,



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Prove that the points and are the vertices of a right-angled triangle.

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If the vertices A, B, C of a triangle ABC are the points with position vectors respectively, what are the vectors determined by its sides? Find the length of these vectors.

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Find the position vector of a point R which divides the line segment joining points and in the ratio 2 : 1.

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