Prove that

i.

ii.

i.

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

Hence,

To Prove :

Formulae :

a) Dot Products :

i)

ii)

b) Cross Products :

i)

ii)

iii)

c) Scalar Triple Product :

Now,

(i)

…………

= 1 …………

………… eq(1)

(ii)

…………

= 1 …………

………… eq(2)

(iii)

…………

= 1 …………

………… eq(3)

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

ii.

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

Hence,

To Prove :

Formulae :

a) Dot Products :

i)

ii)

b) Cross Products :

i)

ii)

iii)

c) Scalar Triple Product :

Answer :

(i)

…………

= -1 …………

………… eq(1)

(ii)

…………

= -1 …………

………… eq(2)

(iii)

…………

= -1 …………

………… eq(3)

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