सूत्र vector a x vectors(b x c) = vectors(a.b) x vector b - vectors(a.b)vector c को सत्यापन कीजिए,

Question

सूत्र  \(\overrightarrow{a}\times\) \((\overrightarrow{b}\times\overrightarrow{c})\) = \((\overrightarrow{a}.\overrightarrow{c})b\) - \((\overrightarrow{a}.\overrightarrow{b})\vec c\) को सत्यापन कीजिए, जबकि

(i) \(\overrightarrow{a}\) = \(\hat{i} + \hat{j} - 2\hat{k}\), \(\overrightarrow{b}\) = \(2\hat{i} - \hat{j} + \hat{k}\), \(\overrightarrow{c}\) = \(\hat{i} + 3\hat{j} - \hat{k}\)

 (i) \(\overrightarrow{a}\) = \(\hat{i} - 2\hat{j} +\hat{k}\), \(\overrightarrow{b}\) = \(2\hat{i} + \hat{j} -\hat{k}\), \(\overrightarrow{c}\) = \(3\hat{i} +5\hat{j} + 2\hat{k}\)

Answer 1

(i) दिया है :

(ii) दिया है :