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QLDSpecialist MathematicsQuick questions

Unit 3: Mathematical induction, and further vectors, matrices and complex numbers

Quick questions on Vector and Cartesian equations of planes in QCE Specialist Mathematics Unit 3

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is cartesian equation?
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Writing n=(a,b,c)\mathbf{n} = (a, b, c) and r=(x,y,z)\mathbf{r} = (x, y, z), the vector equation becomes
What are plane through three points?
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Given three non-collinear points AA, BB, CC, form two vectors in the plane, AB⃗\vec{AB} and AC⃗\vec{AC}. Their cross product is normal to both, hence normal to the plane:
What is distance from a point to a plane?
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The perpendicular distance from a point P0=(x0,y0,z0)P_0 = (x_0, y_0, z_0) to the plane ax+by+cz+d′=0ax + by + cz + d' = 0 is
What are angle between two planes?
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The angle between two planes equals the angle between their normals. For normals n1\mathbf{n}_1 and n2\mathbf{n}_2,
What is line of intersection?
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Two non-parallel planes meet in a line whose direction is n1×n2\mathbf{n}_1 \times \mathbf{n}_2, since the line lies in both planes and so is perpendicular to both normals. Finding one common point fixes the line.

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