jee-main 2023 Q65

jee-main · India · session2_13apr_shift1 Vectors 3D & Lines Vector Algebra and Triple Product Computation

Let $\vec{a} = \hat{i} + 2\hat{j} + \hat{k}$, $\vec{b} = \hat{i} - \hat{j} + \hat{k}$ and $\vec{c} = \hat{i} + \hat{j} - \hat{k}$. A vector in the plane of $\vec{a}$ and $\vec{b}$ whose projection on $\vec{c}$ is $\frac{1}{\sqrt{3}}$ is
(1) $4\hat{i} - \hat{j} + 4\hat{k}$
(2) $3\hat{i} + \hat{j} - 3\hat{k}$
(3) $2\hat{i} + \hat{j} - 2\hat{k}$
(4) $4\hat{i} + \hat{j} - 4\hat{k}$

Let $\vec{a} = \hat{i} + 2\hat{j} + \hat{k}$, $\vec{b} = \hat{i} - \hat{j} + \hat{k}$ and $\vec{c} = \hat{i} + \hat{j} - \hat{k}$. A vector in the plane of $\vec{a}$ and $\vec{b}$ whose projection on $\vec{c}$ is $\frac{1}{\sqrt{3}}$ is\\
(1) $4\hat{i} - \hat{j} + 4\hat{k}$\\
(2) $3\hat{i} + \hat{j} - 3\hat{k}$\\
(3) $2\hat{i} + \hat{j} - 2\hat{k}$\\
(4) $4\hat{i} + \hat{j} - 4\hat{k}$

Paper Questions

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