Class XI Chapter 12 – Introduction to Three Dimensional Geometry Maths ______________________________________________________________________________ Question 4: Fill in the blanks: (i) The x-axis and y-axis taken together determine a plane known as _______. (ii) The coordinates of points in the XY-plane are of the form _______ (iii) Coordinate planes divide the space into _______ octants. Solution 4: (i) The x-axis and y-axis taken together determine a plane known as XY-plane . (ii) The coordinates of points in the XY-plane are of the form (x,y,o) (iii) Coordinate planes divide the space into eight octants. Exercise 12.2 Question 1: Find the distance between the following pairs of points: (i) (2, 3, 5) and (4, 3, 1) (ii) (-3, 7, 2) and (2, 4, -1) (iii) (-1, 3, -4) and (1, -3, 4) (iv) (2, -1, 3) and (-2, 1, 3) Solution 1: The distance between points P(x1, y1, z1) and P(x2, y2, z2) is given 2 2 2 2 1 2 1 2 1 by PQ= x x y y z z (i) Distance between points (2, 3, 5) and (4, 3, 1) 4 2 3 3 1 5 2 2 2 2 0 4 416 20 2 2 2 2 5 Distance between points (â€“3, 7, 2) and (2, 4, â€“1) 2 3 4 7 1 2 2 2 2 5 3 3 2 2 2 25 99 43 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 ______________________________________________________________________________ (ii) Distance between points (â€“1, 3, â€“4) and (1, â€“3, 4) 1 1 3 3 4 4 2 2 2 2 6 8 2 2 2 436 64 104 2 26 (iii) Distance between points (2, â€“1, 3) and (â€“2, 1, 3) 2 2 1 1 3 3 2 2 2 4 2 0 16 4 20 2 5 2 2 2 Question 2: Show that the points (-2, 3, 5), (1, 2, 3) and (7, 0, -1) are collinear. Solution 2: Let points (â€“2, 3, 5), (1, 2, 3), and (7, 0, â€“1) be denoted by P, Q, and R respectively. Points P, Q, and R are collinear if they lie on a line. 3 1 2 2 2 2 PQ 1 2 23 35 2 2 2 91 4 14 6 2 4 2 2 2 QR 71 02 1 3 2 2 2 36 416 56 2 14 9 3 6 2 2 2 PR 72 03 1 5 2 2 2 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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