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