A) \[-14\]
B) \[7\]
C) \[14\]
D) \[1/7\]
Correct Answer: C
Solution :
Key Idea: If \[\overset{\to }{\mathop{\mathbf{a}}}\,\] and \[\overset{\to }{\mathop{\mathbf{b}}}\,\] are two perpendicular vectors, then\[a-b=0\]. Let\[\overset{\to }{\mathop{\mathbf{a}}}\,=3\widehat{\mathbf{i}}+\lambda \widehat{\mathbf{j}}+\widehat{\mathbf{k}}\] and \[\overset{\to }{\mathop{\mathbf{b}}}\,=2\widehat{\mathbf{i}}-\widehat{\mathbf{j}}+8\widehat{\mathbf{k}}\]. Since, they are perpendicular. \[\Rightarrow \] \[\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,=0\] \[\Rightarrow \] \[(3\widehat{\mathbf{i}}+\lambda \widehat{\mathbf{j}}+\widehat{\mathbf{k}})\cdot (2\widehat{\mathbf{i}}-\widehat{\mathbf{j}}+8\widehat{\mathbf{k}})=0\] \[\Rightarrow \] \[6-\lambda +8=0\] \[\Rightarrow \] \[\lambda =14\]
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