jee-main 2016 Q80

jee-main · India · 09apr Vectors: Cross Product & Distances

Let $\vec{a} = 2\hat{i} + \hat{j} - 2\hat{k}$ and $\vec{b} = \hat{i} + \hat{j}$. Let $\vec{c}$ be a vector such that $|\vec{c} - \vec{a}| = 3$, $|(\vec{a} \times \vec{b}) \times \vec{c}| = 3$ and the angle between $\vec{c}$ and $\vec{a} \times \vec{b}$ is $30^\circ$. Then $\vec{a} \cdot \vec{c}$ is equal to:
(1) $\frac{1}{8}$
(2) $25$
(3) $2$
(4) $5$

Let $\vec{a} = 2\hat{i} + \hat{j} - 2\hat{k}$ and $\vec{b} = \hat{i} + \hat{j}$. Let $\vec{c}$ be a vector such that $|\vec{c} - \vec{a}| = 3$, $|(\vec{a} \times \vec{b}) \times \vec{c}| = 3$ and the angle between $\vec{c}$ and $\vec{a} \times \vec{b}$ is $30^\circ$. Then $\vec{a} \cdot \vec{c}$ is equal to:\\
(1) $\frac{1}{8}$\\
(2) $25$\\
(3) $2$\\
(4) $5$

Paper Questions

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