Math Problem Statement

Find an equation of the line where the planes Q and R intersect. Q: -2x + y - 4z = 1; R: x + y + z = -1

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Vector Geometry
Plane Equations
Cross Product

Formulas

Cross product: \mathbf{a} \times \mathbf{b} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \end{vmatrix}
Parametric equation of a line: \mathbf{r}(t) = \mathbf{r}_0 + t \mathbf{v}

Theorems

Cross product theorem for finding direction vectors
Plane intersection theorem

Suitable Grade Level

Undergraduate-level Linear Algebra or Advanced High School Math