a = i - 2j + 3k, b = -2i + 3j - 4k and c = i - 3j + 5k
Given Vectors :
To Prove : Vectors \(\bar a,\bar b,\bar c\) are coplanar.
i.e. [\(\bar a,\bar b,\bar c\)] = 0
Formulae :
1) Scalar Triple Product:
If
Answer :
For given vectors,
= 1(3) + 2(-6) + 3(3) = 3 – 12 +9 = 0
(∴ [\(\bar a,\bar b,\bar c\)] = 0)
Hence, the vectors \(\bar a,\bar b,\bar c\) are coplanar.
Note : For coplanar vectors \(\bar a,\bar b,\bar c\),
[\(\bar a,\bar b,\bar c\)] = 0
