# Given the vectors $\overrightarrow{v_{1}}=\hat{\imath}+3 \hat{\jmath} ; \vec{v}_{2}=2 \hat{\imath}-4 \hat{\jmath}+3 \hat{k},$ the vector $\overrightarrow{v_{3}}$ that is perpendicular to both $\overrightarrow{v_{1}}$ and $\overrightarrow{v_{2}}$ is given by: (A) $\overrightarrow{v_{3}}=\overrightarrow{v_{1}}-\left(\overrightarrow{v_{1}} \cdot \overrightarrow{v_{2}}\right) \frac{\overrightarrow{v_{2}}}{\left|\overrightarrow{v_{2}}\right|}$ (B) $\overrightarrow{v_{3}}=\hat{k}$ (C) $\overrightarrow{v_{3}}=\overrightarrow{v_{2}}-\left(\overrightarrow{v_{1}} \cdot \overrightarrow{v_{2}}\right) \frac{\overrightarrow{v_{1}}}{\mid \overrightarrow{v_{1} \mid}}$ (D) $\overrightarrow{v_{3}}=\frac{\overrightarrow{v_{1}} \times \overrightarrow{v_{2}}}{\left|\overrightarrow{v_{1}} \times \overrightarrow{v_{2}}\right|}$

## Question ID - 155550 | SaraNextGen Top Answer Given the vectors $\overrightarrow{v_{1}}=\hat{\imath}+3 \hat{\jmath} ; \vec{v}_{2}=2 \hat{\imath}-4 \hat{\jmath}+3 \hat{k},$ the vector $\overrightarrow{v_{3}}$ that is perpendicular to both $\overrightarrow{v_{1}}$ and $\overrightarrow{v_{2}}$ is given by: (A) $\overrightarrow{v_{3}}=\overrightarrow{v_{1}}-\left(\overrightarrow{v_{1}} \cdot \overrightarrow{v_{2}}\right) \frac{\overrightarrow{v_{2}}}{\left|\overrightarrow{v_{2}}\right|}$ (B) $\overrightarrow{v_{3}}=\hat{k}$ (C) $\overrightarrow{v_{3}}=\overrightarrow{v_{2}}-\left(\overrightarrow{v_{1}} \cdot \overrightarrow{v_{2}}\right) \frac{\overrightarrow{v_{1}}}{\mid \overrightarrow{v_{1} \mid}}$ (D) $\overrightarrow{v_{3}}=\frac{\overrightarrow{v_{1}} \times \overrightarrow{v_{2}}}{\left|\overrightarrow{v_{1}} \times \overrightarrow{v_{2}}\right|}$

(D) $\overrightarrow{v_{3}}=\frac{\overrightarrow{v_{1}} \times \overrightarrow{v_{2}}}{\left|\overrightarrow{v_{1}} \times \overrightarrow{v_{2}}\right|}$