Prove the following


A vector $\vec{a}=\alpha \hat{i}+2 \hat{j}+\beta \hat{k}(\alpha, \beta \in R)$ lies in the plane of the vectros $\vec{b}=\hat{i}+\hat{j}$ and $\vec{c}=\hat{i}-\hat{j}+4 \hat{k}$.

If $\vec{a}$ bisects the angle between $\vec{b}$ and $\vec{c}$, then:

  1. $\vec{a} \cdot \hat{i}+1=0$

  2. $\overrightarrow{\mathrm{a}} \cdot \hat{\mathrm{i}}+3=0$

  3. $\overrightarrow{\mathrm{a}} \cdot \hat{\mathrm{k}}+4=0$

  4. $\vec{a} \cdot \hat{k}+2=0$

Correct Option: , 4


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