Question

What is the value of Δ if, Δ = `|(0, sin alpha, - cos alpha),(-sin alpha, 0, sin beta),(cos alpha, - sin beta, 0)|` 

Options

• Zero

• 1

• 2

• 3

Answer 1

Zero

Explanation:

Expending along R₁ we get,

Δ = `0|(0, sin beta),(- sin beta, 0)| - sin alpha |(- sin alpha, sin beta),(cos alpha, 0)| - cos alpha |(- sin alpha, 0),(cos alpha, - sin beta)|`

= `0 - sin alpha(0 - sin beta cos alpha) - cos alpha (sin alpha sin beta - 0)`

= `sin alpha sin beta cos alpha - cos alpha sin alpha sin beta` = 0