jee-main 2023 Q76

jee-main · India · session2_10apr_shift1 Vectors Introduction & 2D Dot Product Computation

Let $O$ be the origin and the position vector of the point $P$ be $-\hat{i} - 2\hat{j} + 3\hat{k}$. If the position vectors of the points $A$, $B$ and $C$ are $-2\hat{i} + \hat{j} - 3\hat{k}$, $2\hat{i} + 4\hat{j} - 2\hat{k}$ and $-4\hat{i} + 2\hat{j} - \hat{k}$ respectively, then the projection of the vector $\overrightarrow{OP}$ on a vector perpendicular to the vectors $\overrightarrow{AB}$ and $\overrightarrow{AC}$ is
(1) 3
(2) $\frac{8}{3}$
(3) $\frac{7}{3}$
(4) $\frac{10}{3}$

Let $O$ be the origin and the position vector of the point $P$ be $-\hat{i} - 2\hat{j} + 3\hat{k}$. If the position vectors of the points $A$, $B$ and $C$ are $-2\hat{i} + \hat{j} - 3\hat{k}$, $2\hat{i} + 4\hat{j} - 2\hat{k}$ and $-4\hat{i} + 2\hat{j} - \hat{k}$ respectively, then the projection of the vector $\overrightarrow{OP}$ on a vector perpendicular to the vectors $\overrightarrow{AB}$ and $\overrightarrow{AC}$ is\\
(1) 3\\
(2) $\frac{8}{3}$\\
(3) $\frac{7}{3}$\\
(4) $\frac{10}{3}$

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