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cross product The vector (or cross) product of the vectors a and b is defined to be:
a \times b = |a| |b| \sin \theta \hat{n}
where \theta is the angle between the vectors and \hat{n} is a unit vector perpendicular to both a and b.
The direction of \hat{n} is given by the right-hand rule - see the diagram.

The magnitude the cross product is equal to the area of the parallelogram that the vectors span.

If i, j and k are the familiar unit vectors, then:
i \times j = k, j \times k = i, k \times i = j and
i \times i = 0, j \times j = 0, k \times k = 0

If a = a_1i+a_2j+a_3k \quad and b = b_1i+b_2k+b_3k \quad then: a \times b = (a_2b_3-a_3b_2)i + (a_3b_1-a_1b_3)j + (a_1b_2-a_2b_1)k

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cross product

For vectors a and b, the cross product is the vector c whose magnitude is ab sin C, where C is the angle between the directions of the vectors, and which is perpendicular to both a and b.


A measure of the size of a mathematical object


one line being at right angles to another.


A method for connecting one value with another.


The union of two sets A and B is the set containing all the elements of A and B.

unit vector

A vector with magnitude equal to 1.


A mathematical object with magnitude and direction.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)FP4VectorsCross product-
AQA A2 Further Maths 2017Pure MathsVectorsCross Product-
AQA AS/A2 Further Maths 2017Pure MathsVectorsCross Product-
CBSE XII (India)Vectors and 3-D GeometryVectorsCross product definition, geometrical interpretation, properties and application-
CCEA A-Level (NI)FP3VectorsCross product-
Edexcel A-Level (UK - Pre-2017)FP3VectorsCross product-
Edexcel AS Further Maths 2017Further Pure 1VectorsCross Product-
Edexcel AS/A2 Further Maths 2017Further Pure 1VectorsCross Product-
I.B. Higher Level4VectorsCross product-
Methods (UK)M4VectorsCross product-
OCR A-Level (UK - Pre-2017)FP3VectorsCross product-
OCR AS Further Maths 2017Pure CoreVectorsCross Product-
OCR MEI A2 Further Maths 2017Core Pure BVectors and 3-D SpaceCross Product-
OCR-MEI A-Level (UK - Pre-2017)FP3VectorsCross product-
Pre-Calculus (US)E1VectorsCross product-
Scottish Advanced HighersM3VectorsCross product-
Scottish (Highers + Advanced)AM3VectorsCross product-
Universal (all site questions)VVectorsCross product-