Question

The base vectors (a₁, a₂, a₃)  are given in terms of base vectors (b₁, b₂, b₃) as,

vector a₁ = 2b₁ + 3b₂ - b₃;

vector a₂ = b₁ - 2b₂ + 2b₃ & a₃ = - 2b₁ + b₂ - 2b₃.

If vector F = 3b₁ - b₂ + 2b₃. then express F in terms of a₁, a₂, a₃.

Answer 1

vector a₁ = vector (2b₁ + 3b₂ - b₃)

vector a₂ = vector(b₁ - 2b₂ + 2b₃)

vector a₃ = vector(3b₁ - b₂ + 2b₃)

On solving, we get vector F = vector(2a₁ + 5a₂ + 3a₃)