Question

Given two planes how do I find the vector equation?

Answer 1

The vector equation for the intersection of the two planes is given by:

9i + 36j - 24k.

What is the vector equation for the intersection of two planes?

Suppose that we have two planes, defined as follows:

• ax + by + cz = K1. (K1 constant).

• dx + ey + fz = K2. (K2 constant).

The vector equation for the intersection between these two places is given by the determinant of the following matrix:

$\left[\begin{array}{ccc}i&j&k\\a&b&c\\d&e&f\end{array}\right]$

For this problem, the planes are:

• 6y + 9z = 39.

• 4x + 3y + 6z = 10.

Hence the matrix of which we have to find the determinant is:

$\left[\begin{array}{ccc}i&j&k\\0&6&9\\4&3&6\end{array}\right]$

The determinant of the 3 x 3 matrix is given by:

D = i x  6 x 6 + j x 9 x 4 + k x 0 x 3 - (k x 6 x 4 + j x 0 x 6 + i x 9 x 3).

D = 36i + 36j - (24k + 27i)

D = 36i + 36j - 24k - 27i

D = 9i + 36j - 24k.

Which is the vector equation.

More can be learned about the vector equation for the intersection of the two planes at https://brainly.com/question/8837203

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