For what value of $x$ will the two vectors $\vec{A} = 2\hat{i} + 2\hat{j} - x\hat{k}$ and $\vec{B} = 2\hat{i} - \hat{j} - 3\hat{k}$ be perpendicular to each other?
- A$x = 2/3$
- B$x = 3/2$
- C$x = -4/3$
- D$x = -2/3$
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If $|\vec A| = 2$ and $|\vec B| = 4$,then match the relation in Column $-I$ with the angle $\theta$ between $\vec A$ and $\vec B$ in Column $-II$.
Column $-I$ Column $-II$ $(a) \vec A \cdot \vec B = 0$ $(i) \theta = 0^\circ$ $(b) \vec A \cdot \vec B = +8$ $(ii) \theta = 90^\circ$ $(c) \vec A \cdot \vec B = 4$ $(iii) \theta = 180^\circ$ $(d) \vec A \cdot \vec B = -8$ $(iv) \theta = 60^\circ$
| Column $-I$ | Column $-II$ |
| $(a) \vec A \cdot \vec B = 0$ | $(i) \theta = 0^\circ$ |
| $(b) \vec A \cdot \vec B = +8$ | $(ii) \theta = 90^\circ$ |
| $(c) \vec A \cdot \vec B = 4$ | $(iii) \theta = 180^\circ$ |
| $(d) \vec A \cdot \vec B = -8$ | $(iv) \theta = 60^\circ$ |
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View SolutionIf the vector $2\hat{i} + 3\hat{j} + 8\hat{k}$ is perpendicular to the vector $4\hat{j} - 4\hat{i} + \alpha\hat{k}$,then what is the value of $\alpha$?
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