Product of three or four vector

Product Of Three Or Four Vector

TOPIC INVOLVE IN NOTES

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* a.b = |a| |b| cosθ

* axb = |a| |b| sinθ

If we have two vectors a = a1, a2, a3…..an and b = b1, b2, b3…..bn, then the dot product is given by

a . b = a 1 b 1 + a 2 b 2 + a 3 b 3 + \dots . . + a n b n = \sum j = 1 n a j b j

A⃗
A⃗

a.(bxc) = scalar triple product

a.(b.c) = not defined

ax(bxc) = vector triple product

ax(b.c) = not defined

a(b.c) = defined

a(bxc) = not defined

(axb).(cxd) = scalar product of four vector

(axb)x(cxd) = vector product of four vector

scalar triple product [abc]=a.(bxc)

volume of the parallelopiped = area of the base parallelopiped X height of the parallelopiped

vector triple product [abc] = a(bxc)

scalar product of four vector

| a.c a.d |

(axb).(cxd) = | b.d c.d |

reciprocal system of vectors

-> let a, b, c be any three non-coplanar vectors such that [abc] is not equal to 0. then reciprocal system of a, b, c is defined as

a' = bxc b' = cxa c' = axb

[abc] [abc] [abc]

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