← Further Maths syllabus

EnglandFurther Maths

Core Pure: further vectors and planes

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you find angles between lines and planes and the shortest distances in three dimensions?

Angles between two lines, between a line and a plane, and between two planes, and the shortest distance from a point to a line or plane and between two skew lines.
A focused answer to the OCR A-Level Further Mathematics A content on distances and angles in three dimensions, covering the angle between two lines, between a line and a plane and between two planes, and the shortest distance from a point to a line or plane and between two skew lines, using the scalar and vector products.
12 min answer →

How do you write the equation of a line in three dimensions, and how do you find where two lines meet?

The vector and Cartesian equations of a straight line in three dimensions, the direction vector, and finding the intersection of two lines or showing that they are parallel or skew.
A focused answer to the OCR A-Level Further Mathematics A content on the equations of lines in three dimensions, covering the vector equation with a point and a direction vector, the Cartesian (symmetric) form, and finding the intersection of two lines or determining that they are parallel, intersecting or skew.
11 min answer →

How do you write the equation of a plane, and how do you find where a line meets a plane or where two planes meet?

The vector, scalar product and Cartesian equations of a plane, the normal vector, and the intersection of a line with a plane and of two planes.
A focused answer to the OCR A-Level Further Mathematics A content on the equations of planes, covering the vector, scalar product (r dot n) and Cartesian forms, the normal vector and how to find it from the cross product, and finding the intersection of a line with a plane and the line of intersection of two planes.
11 min answer →

How do the scalar and vector products work, and what geometric information do they give?

The scalar (dot) product and its use for angles and perpendicularity, the vector (cross) product and its use for a perpendicular direction and areas, and the modulus of the vector product as an area.
A focused answer to the OCR A-Level Further Mathematics A content on the scalar and vector products, covering the dot product and its use for the angle between vectors and for testing perpendicularity, the cross product and its use to find a vector perpendicular to two given vectors, and the modulus of the cross product as the area of a parallelogram or triangle.
11 min answer →