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BITSAT2012MathematicsThree Dimensional GeometryActual

The foot of the perpendicular from the point (7,14,5) to the plane 2 x +4 y - z =2 are

Options

  1. A(1,2,8)
  2. B(3,2,8)
  3. C(5,10,6)
  4. D(9,18,4)

Correct answer

A. (1,2,8)

Step-by-step solution

We know that the length of the perpendicular from the point (x₁, y₁, z₁ ) to the plane a x+b y+c z+d=0 is |a x₁+b y₁+c z₁+d | a²+b²+c² and the co-ordinate ( , , ) of the foot of the are given by -x₁ a = -y₁ b = -z₁ c =- ( a x₁+b y₁+c z₁+d a²+b²+c² ) ...(1) In the given ques, x₁=7, y₁=14, z₁=5 , a=2 b=4, c=-1, d=-2 By putting these values in (1), we get -7 2 = -14 4 = -5 -1 =- 63 21 =1, =2 and =8 Hence, foot of is (1,2,8)

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