VITEEE 2012 Paper

a = i + j + k,6 = i + 3j + 5k
and c = 7i + 9j + 11 k
Let A=a + b
= (i + j + k) + (i + 3j + 5k)
= 2i + 4j + 6k and B = b + c
= (i + 3 j +5k) + (7i + 9j + 11 k)
= 8i+ 12j + 16k
∴ Area of parallelogram
=

1

2

|A × B|
(Since A and B are diagonals)
=

1

2

|

i	j	k
2	4	6
8	12	16

|
=

1

2

|i (64 - 72) - j (32 - 48) + k (24 - 32)|
=

1

2

|- 8i + 16j - 8k|
= √(−4)2+(8)2+(−4)2
= √96 = 4√6 sq units