A) \[-3/2\]
B) \[6\]
C) \[-6\]
D) \[3\]
Correct Answer: A
Solution :
Let \[\vec{a}=x\hat{i}+\hat{j}+\hat{k}\] and \[\vec{b}=2\hat{i}-\hat{j}+5\hat{k}\] and projection of \[\vec{a}\] on \[\vec{b}=\frac{1}{\sqrt{30}}\] \[\Rightarrow \] \[\frac{\vec{a}.\vec{b}}{|\vec{b}|}=\frac{1}{\sqrt{30}}\] \[\Rightarrow \] \[\frac{(x\hat{i}+\hat{j}+\hat{k}).(2\hat{i}-\hat{j}+5\hat{k})}{|\sqrt{4+1+25}|}=\frac{1}{\sqrt{30}}\] \[\Rightarrow \] \[2x-1+5=\frac{\sqrt{30}}{\sqrt{30}}=1\] \[\Rightarrow \] \[2x=-3\] \[\Rightarrow \] \[x=-\frac{3}{2}\]
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