AS/A2 Pure 4 Pure 5

P6 Topic 3: Vectors
Cross product definition
The vector (or cross) product of the vectors a and b is defined to be:
a × b = |a| |b| sin q n
where q is the angle between the vectors and n is a unit vector perpendicular to both a and b. If i, j and k are the familiar unit vectors, then:
i × j = k j × k = i k × i = j		i × i = 0 j × j = 0 k × k = 0
If a = a1i+a2j+a3k and b = b1i+b2j+b3k then:
a × b = (a2b3-a3b2)i+ (a3b1-a1b3)j + (a1b2-a2b1)k

Summary a × b = |a| |b| sin q n a × b = (a2b3-a3b2)i+ (a3b1-a1b3)j + (a1b2-a2b1)k a × b = -b × a If a × b = 0, then either a=0 or b=0 or a and b are parallel This page uses HotEqn.