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Q.65 Let PQR be a triangle with R(-1, 4, 2). Suppose M (2, 1, 2) is the mid-point of PQ. The distance of the centroid of ΔPQR from the point of intersection of the lines (x−2)/0 = y/2 = (z+3)/(−1) and (x−1)/1 = (y+3)/(−3) = (z+1)/1 is-

1. √69
2. 69
3. √99
4. 9

Correct answer: √69

Solution

The centroid of triangle PQR can be calculated using the coordinates of its vertices, and the distance from this centroid to the intersection point of the given lines can be determined using the distance formula. The calculations yield a distance of √69, confirming that this option is correct.

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