Q. 275.0( 1 Vote )

Find the vector e

Answer :

Let the position vectors of the three points be



So, the equation of the plane passing through the points is







Now, we know that, In cross product









…(i)


So, the vector equation of the required plane is


The equation of the given line is


Position vector of any point on the give line is


…(ii)


The point (ii) lies on plane (i) if,



9(3 + 2λ) + 3(-1 - 2λ) – 1(-1 + λ) = 14


27 + 18λ – 3 - 6λ + 1 – λ = 14


11λ + 25 = 14


11λ = 14 – 25


11λ = -11


λ = -1


Putting λ = -1 in eq. (ii), we get





Thus, the position vector of the point of intersection of the given line and the plane (i) is and its coordinates are (1, 1, -2)


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