A mobile tower stands at the top of a hill. Consider the surface on which the tower stands as a plane having points A (1, 0, 2),
B (3, –1, 1) and C (1, 2, 1) on it. The mobile tower is tied with 3 cables from the point A, B and C such that it stands vertically on the ground. The top of the tower is at the point (2, 3, 1) as shown in the figure.

A mobile tower stands at the top - Teachoo.jpg

Based on the above answer the following:

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Question 1

The equation of the plane passing through the points A, B and C is

(a) 3x – 2y + 4z = –11

(b) 3x + 2y + 4z = 11

(c) 3x – 2y – 4z = 11

(d) –3x + 2y + 4z = –11

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Question 2

The height of the tower from the ground is

(a) 5/√29 units

(b) 7/√29 units

(c) 6/√29 units

(d) 8/√29 units

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Question 3

The equation of the perpendicular line drawn from the top of the tower to the ground is

(a) (x - 1)/2=(y + 3)/1=(z - 5)/(-2)

(b) (x - 2)/(-3)=(y - 3)/2=(z - 1)/(-4)

(c) (x - 2)/3=(y - 3)/2=(z - 1)/4

(d) (x + 1)/(-2)=(y + 3)/(-1)=(z - 5)/2

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Question 4

The coordinates of the foot of the perpendicular drawn from the top of the tower to the ground are

(a) (43/29,(-77)/29,(-9)/29)

(b) (9/7,(-1)/7,(-10)/7)

(c) ((-43)/29,(-77)/29,(-9)/29)

(d) (43/29,77/29,9/29)

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Question 5

The area of ∆ 𝐴𝐵𝐶 is

(a) √29/4 units

(b) √29/2 units

(c) √39/2 units

(d) √39/4 units

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  1. Chapter 11 Class 12 Three Dimensional Geometry (Term 2)
  2. Serial order wise

Transcript

Question A mobile tower stands at the top of a hill. Consider the surface on which the tower stands as a plane having points A (1, 0, 2), B (3, –1, 1) and C (1, 2, 1) on it. The mobile tower is tied with 3 cables from the point A, B and C such that it stands vertically on the ground. The top of the tower is at the point (2, 3, 1) as shown in the figure. Based on the above answer the following:Question 1 The equation of the plane passing through the points A, B and C is (a) 3x – 2y + 4z = –11 (b) 3x + 2y + 4z = 11 (c) 3x – 2y – 4z = 11 (d) –3x + 2y + 4z = –11(b) 3x + 2y + 4z = 11 Question 2 The height of the tower from the ground is (a) 5/√29 units (b) 7/√29 units (c) 6/√29 units (d) 8/√29 units(a) 5/√29 units Question 3 The equation of the perpendicular line drawn from the top of the tower to the ground is (a) (𝑥 − 1)/2=(𝑦 + 3)/1=(𝑧 − 5)/(−2) (b) (𝑥 − 2)/(−3)=(𝑦 − 3)/2=(𝑧 − 1)/(−4) (c) (𝑥 − 2)/3=(𝑦 − 3)/2=(𝑧 − 1)/4 (d) (𝑥 + 1)/(−2)=(𝑦 + 3)/(−1)=(𝑧 − 5)/2 (c) (𝑥 − 2)/3=(𝑦 − 3)/2=(𝑧 − 1)/4 Question 4 The coordinates of the foot of the perpendicular drawn from the top of the tower to the ground are (a) (43/29,(−77)/29,(−9)/29) (b) (9/7,(−1)/7,(−10)/7) (c) ((−43)/29,(−77)/29,(−9)/29) (d) (43/29,77/29,9/29)(d) (43/29,77/29,9/29) Question 5 The area of ∆ 𝐴𝐵𝐶 is (a) √29/4 units (b) √29/2 units (c) √39/2 units (d) √39/4 units(b) √29/2 units

About the Author

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.