A) 60
B) 64
C) 74
D) ? 74
Correct Answer: D
Solution :
\[\mathbf{\alpha }\,.\,[\,\mathbf{\gamma }\times (\mathbf{\alpha }\times \mathbf{\beta })]\]\[=\mathbf{\alpha }\,.\,[(\mathbf{\gamma }\,.\,\mathbf{\beta })\mathbf{\alpha }-(\mathbf{\gamma }\,.\,\mathbf{\alpha })\,\mathbf{\beta }]\] \[={{(\mathbf{\alpha })}^{2}}(\mathbf{\gamma }\,.\,\mathbf{\beta })-(\mathbf{\gamma }\,.\,\mathbf{\alpha })(\mathbf{\beta }\,.\,\mathbf{\alpha })\]\[=14(-3)-(4)(8)=-74\].
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