# Prove that i. [i  j  k] = [j  k  i] = [k  i  j] = 1 ii. [i  k  j] = [k  j  i] = [j  i  k] = -1

133 views
in Vectors
closed

Prove that

i. [i  j  k] = [j  k  i] = [k  i  j] = 1

ii. [i  k  j] = [k  j  i] = [j  i  k] = -1

+1 vote
by (50.8k points)
selected by

i. [i  j  k] = [j  k  i] = [k  i  j] = 1

Let, i, j, k be unit vectors in the direction of positive X -axis, Y -axis, Z -axis respectively.

Hence, Formulae :

a) Dot Products : b) Cross Products : c) Scalar Triple Product : From eq(1), eq(2) and eq(3),

[i  j  k] = [j  k  i] = [k  i  j] = 1

Hence Proved.

Notes :

1. A cyclic change of vectors in a scalar triple product does not change its value i.e. 2. Scalar triple product of unit vectors taken in a clockwise direction is 1, and that of unit vectors taken in anticlockwise direction is -1 Let, i, j, k be unit vectors in the direction of positive X -axis, Y -axis, Z -axis respectively.

Hence, Formulae :

a) Dot Products : b) Cross Products : c) Scalar Triple Product :  From eq(1), eq(2) and eq(3), Hence Proved.

Notes :

1. A cyclic change of vectors in a scalar triple product does not change its value i.e. 2. Scalar triple product of unit vectors taken in a clockwise direction is 1, and that of unit vectors taken in anticlockwise direction is -1 +1 vote