99 Percentile Qs Bank for JEE MainMathematicsThree Dimensional Geometry

The length of the perpendicular (in units) from the point 1,2 , 4 on the straight line x - 2 1 = y - 7 2 = z - 3 - 1 lies in the interval

Options

A1 , 3 2
B2,3
C0,2
D4,5

Correct answer

C. 0,2

Step-by-step solution

Let, point A is 1,2 , 4 and any general point on the line is B λ + 2,2 λ + 7 , - λ + 3 , A B → = λ + 1 i ^ + 2 λ + 5 j ^ + - λ - 1 k ^ and a vector parallel to the line is b → = i ^ + 2 j ^ - k ^ A B → ⋅ b → = 0 ⇒ λ + 1 + 4 λ + 10 + λ + 1 = 0 ⇒ λ = - 2 The length of the perpendicular = A B → = - 2 + 1 2 + - 4 + 5 2 + 2 - 1 2 = 3 units

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