A) \[\frac{5}{7}\]
B) \[\frac{5}{3\sqrt{3}}\]
C) \[\frac{7}{6\sqrt{6}}\]
D) \[\frac{7}{6\sqrt{3}}\]
Correct Answer: D
Solution :
[d] \[v=\left[ \vec{a}\vec{b}\vec{c} \right]\] \[\Rightarrow 2-1(5)+\lambda (1)=\pm 1\] \[\Rightarrow \lambda -3=1\] or \[\lambda -3=-1\] \[\Rightarrow \lambda =4\,\,\text{or}\,\,2\] \[\vec{u}=\hat{i}+\hat{j}+4\hat{k}\] or \[\hat{i}+\hat{j}+2\hat{k}\] \[\therefore \cos \theta =\frac{2+1+4}{\sqrt{18}\sqrt{6}}or\frac{2+1+2}{\sqrt{6}\sqrt{6}}\] \[=\frac{7}{6\sqrt{3}}\,\,\text{or}\,\,\frac{5}{6}\]You need to login to perform this action.
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