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प्रश्न
If the vectors \[3 \hat{i} + \lambda \hat{j} + \hat{k} \text{ and } 2 \hat{i} - \hat{j} + 8 \hat{k}\] are perpendicular, then λ is equal to
विकल्प
(a) −14
(b) 7
(c) 14
(d) \[\frac{1}{7}\]
उत्तर
(c) 14
\[\text{ It is given that vectors }3 \hat{i} + \lambda \hat{j} + \hat{k} \text{ and } 2 \hat{i} - \hat{j} + 8 \hat{k} \text{ are perpendicular }.\]
\[\text{ So, their dot product is zero }.\]
\[\left( 3 \hat{i} + \lambda \hat{j} + \hat{k} \right) . \left( 2 \hat{i} - \hat{j} + 8 \hat{k} \right) = 0\]
\[ \Rightarrow 6 - \lambda + 8 = 0\]
\[ \Rightarrow 14 - \lambda = 0\]
\[ \therefore \lambda = 14\]
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