Let r be the position vector of a point in the Cartesian OX Y plane such that r ⋅ ( 10 j ^ − 8 i ^ − r ) = 40 , max { ∣ r + 2 i ^ − 3 j ^ ∣ 2 } = l and min { ∣ r + 2 i ^ − 3 j ^ ∣ 2 } = m . A ta

Question

Let r be the position vector of a point in the Cartesian OX Y plane such that r ⋅ ( 10 j ^ ​ − 8 i ^ − r ) = 40 , max { ∣ r + 2 i ^ − 3 j ^ ​ ∣ 2 } = l and min { ∣ r + 2 i ^ − 3 j ^ ​ ∣ 2 } = m . A tangent line is drawn to the curve y = x 2 8 ​ at the point A with abscissa 2. The tangent cuts the x -axis at B . The value of A B ⋅ OB ( O is the origin) is

TestHub · Accepted Answer

At x = 2 , y = 4 8 ​ = 2 , so A ( 2 , 2 ) . d x d y ​ = − x 3 16 ​ = − 2 at x = 2 . The tangent is y − 2 = − 2 ( x − 2 ) , that is 2 x + y − 6 = 0 , which cuts the x -axis at B ( 3 , 0 ) . A B = i ^ − 2 j ^ ​ and OB = 3 i ^ , so A B ⋅ OB = 3 .

Mathematics - Application of Derivative Question with Solution | TestHub

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