Q. 275.0( 1 Vote )

# Find the vector e

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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