query: Find a vector v⃗ parallel to the intersection of the planes 2x+y+5z=3 and 4x+2y+2z=7.
positive_passages.docid: 143334
positive_passages.text: Find a vector parallel to the line of intersection of the two given planes.
negative_passages.docid: 37478
negative_passages.text: Write the equation of the parabola that has the vertex at point $(5,0)$ and passes through the point $(7,−2)$.
negative_passages.docid: 133123
negative_passages.text: Find the Unit Vector of a Three Dimensional Vector
negative_passages.docid: 135479
negative_passages.text: Two-dimensional Vectors Problem
negative_passages.docid: 65964
negative_passages.text: Prove that the line joining the midpoint of parallel sides of a trapezium passes through the point of intersection of diagonals
negative_passages.docid: 116223
negative_passages.text: Show that the angles satisfy $x+y=z$
negative_passages.docid: 30331
negative_passages.text: Steps to solve this system of equations: $\sqrt{x}+y=7$, $\sqrt{y}+x=11$
negative_passages.docid: 142862
negative_passages.text: Intersection of an ellipsoid and plane in parametric form
negative_passages.docid: 64243
negative_passages.text: How to find a 4D vector perpendicular to 3 other 4D vectors?
negative_passages.docid: 133043
negative_passages.text: Find the equation of the plane passing through a point and a vector orthogonal
negative_passages.docid: 120641
negative_passages.text: Intersection of three vector subspaces
negative_passages.docid: 62180
negative_passages.text: Best way to find the intersection of multiple sets?
negative_passages.docid: 6547
negative_passages.text: Given $3$-dimensional subspaces $V, W \subset \Bbb R^5$, there is a nonzero vector in $V \cap W$
negative_passages.docid: 131688
negative_passages.text: Solve $\sin 7x+\sin 3x=0$
negative_passages.docid: 79292
negative_passages.text: How to calculate the intersection of two planes?
negative_passages.docid: 30246
negative_passages.text: Find the equation of the tangent plane to the surface $x^{\frac{2}{3}}+y^{\frac{2}{3}}+z^{\frac{2}{3}}=2^{\frac{2}{3}}$ at $(x_0,y_0,z_0)$
negative_passages.docid: 32424
negative_passages.text: How can I calculate the angle and proper turn direction between two 2D vectors?