Show that the points (2, 0, 1), (0,4,-3) and (-2, 5, 0) are non-collinear. Hence find the equation of plane passing through them ?
Please provide guideline with answer.
Please provide guideline with answer.
1 Answer
The scalar equation of the plane that contains all 3 points is:
Explanation:
Let
Let
Compute the dot-product by multiplying the respective components:
Compute the magnitudes:
Use the equation,
If the points were co-linear, then the cosine of the angle between their vectors would have been
Use the cross-product to find a vector that is perpendicular to both vectors. I use a 5 column determinant to compute the cross-product.
First the major diagonals:
Subtract from that the minor diagonals:
Divide the vector by 2:
These coefficients match the coefficients for
To determine the value of c, substitute in one of the points. I shall use the first one:
The scalar equation of the plane that contains all 3 points is: