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# Prove the following

Question:

Let $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}$ be two vectors. If $\vec{c}$ is a vector such that $\vec{b} \times \vec{c}=\vec{b} \times \vec{a}$ and $\overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{a}}=0$, then $\overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{b}}$ is equal to

1. $\frac{1}{2}$

2. $-1$

3. $-\frac{1}{2}$

4. $-\frac{3}{2}$

Correct Option: , 3

Solution: