Class XI Chapter 12 – Introduction to Three Dimensional Geometry Maths ______________________________________________________________________________ Question 3: If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (-4, 3b, -10) and R (8, 14, 2c), then find the values of a, b and c. Solution 3: It is known that the coordinates of the centroid of the triangle, whose vertices are (x1, y1, z1), (x2, 1 2 3 1 2 3 1 2 3 y2, z2) and (x3, y3, z3), are x x x , y y y , z z z 3 3 3 Therefore, coordinates of the centroid of 2a 48 23b 14 610 2c 2a 4 3b 16 2c 4 ΔPQR = , , , , 3 3 3 3 3 3 It is given that origin is the centroid of ΔPQR. 2a 4 3b 16 2c 4 0,0,0, , , 3 3 3 2a 4 3b 16 2c 4 0, 0 and 0 3 3 3 16 a 2, b andc 2 3 Thus, the respective values of a, b, and c are -2, - 16 , and , 2. 3 Question 4: Find the coordinates of a point on y-axis which are at a distance of 5 2 from the point P (3, â€“2, 5). Solution 4: If a point is on the y-axis, then x-coordinate and the z-coordinate of the point are zero. Let A (0, b, 0) be the point on the y-axis at a distance of 5 2 from point P (3, â€“2, 5). Accordingly, AP = 5 2 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 12 – Introduction to Three Dimensional Geometry Maths ______________________________________________________________________________ 2 AP 50 b 2 2 2 30 2 50 50 2 9 4 b 4b 25 50 2 b b 4 12 0 2 b b b 6 2 12 0 b b 6 2 0 b 6or 2 Thus, the coordinates of the required points are (0, 2, 0) and (0, â€“6, 0). Question 5: A point R with x-coordinate 4 lies on the line segment joining the points P (2, â€“3, 4) and Q (8, 0, 10). Find the coordinates of the point R. [Hint suppose R divides PQ in the ratio k: 1. The coordinates of the point R are given by 8k 2 3 10k 4 , , k 1 k 1 k 1 ] Solution 5: The coordinates of points P and Q are given as P (2, â€“3, 4) and Q (8, 0, 10). Let R divide line segment PQ in the ratio k:1. Hence, by section formula, the coordinates of point R are given by k 8 2 0 3 10 4 8 2 3 10 4 , k , k k , , k k 1 k 1 k 1 k 1 k 1 k 1 It is given that the x-coordinate of point R is 4. 8k 2 4 k 1 8k 2 4k 4 4k 2 1 k 2 1 10 4 3 2 4, , 4, 2,6 1 1 1 1 2 2 Therefore, the coordinates of point R are Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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