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If the mid-points of the sides of a triangle AB; BC; CA are D (1, 2, – 3), E (3, 0, 1) and F (–1, 1, – 4), then the centriod of the triangle ABC is ________.

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The plane parallel to yz - plane is perpendicular to ________.

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The length of the longest piece of a string that can be stretched straight in a rectangular room whose dimensions are 10, 13 and 8 units are ______.

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If the distance between the points (a, 2, 1) and (1, –1, 1) is 5, then a _______.

Match each item given under the column C₁ to its correct answer given under column C₂.

Column C₁

(a) In xy-plane

(b) Point (2, 3,4) lies in the

(c) Locus of the points having x coordinate 0 is

(d) A line is parallel to x-axis if and only

(e) If x = 0, y = 0 taken together will represent the

(f) z = c represent the plane

(g) Planes x = a, y = b represent the line

(h) Coordinates of a point are the distances from the origin to the feet of perpendiculars

(i) A ball is the solid region in the space enclosed by a

(j) Region in the plane enclosed by a circle is known as a

Column C₂

i) Ist octant

ii) yz-plane

iii) z-coordinate is zero

iv) z-axis

v) plane parallel to xy-plane

vi) if all the points on the line have equal y and z-coordinates

vii) from the point on the respective axis

viii) parallel to z - axis.

ix) Disc

x) Sphere