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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.

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Based on the above answer the following:

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Question 1
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## 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
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## 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
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## 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
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## 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
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## The area of ∆ 𝐴𝐵𝐶 is

## (a) √29/4 units

## (b) √29/2 units

## (c) √39/2 units

## (d) √39/4 units