If ` veca, vecb, vecc and vecd ` ar distinct vectors such that `veca xx vecc = vecb xx vecd and veca xx vecb = vecc xx vecd`. Prove that `(veca-vecd).(vecc-vecb)ne 0, i.e., veca.vecb + vecd.vecc nevecd.vecb + veca.vecc.`

Explanation

To prove that \((\vec{a} - \vec{d}) \cdot (\vec{c} - \vec{b}) \neq 0\), we start with the given conditions:

1. \(\vec{a} \times \vec{c} = \vec{b} \times \vec{d}\) (Equation 1)
2. \(\vec{a} \times \vec{b} = \vec{c} \times \vec{d}\) (Equation 2)

### Step 1: Subtract Equation 2 from Equation 1

We will subtract Equation 2 from Equation 1:
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