The component of a vector $\vec{A}$ along a direction making an angle $\theta$ with it is given by $A \cos \theta$. What can be said about the magnitude of this component?
- AAlways less than or equal to its magnitude
- BAlways greater than its magnitude
- CAlways equal to its magnitude
- DNone of the above
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The resultant of two vectors $\vec{A}$ and $\vec{B}$ makes an angle $\alpha$ with $\vec{A}$ and an angle $\beta$ with $\vec{B}$. Which of the following is true?
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Column $I$ Column $II$ $(A)$ Component along $x$-axis $(p)$ $5 \text{ unit}$ $(B)$ Component along vector $(2 \hat{i} + \hat{j} + 2 \hat{k})$ $(q)$ $4 \text{ unit}$ $(C)$ Component along $(6 \hat{i} + 8 \hat{j} - 10 \hat{k})$ $(r)$ $0$ $(D)$ Component along $(-3 \hat{i} - 4 \hat{j} + 5 \hat{k})$ $(s)$ None
| Column $I$ | Column $II$ |
|---|---|
| $(A)$ Component along $x$-axis | $(p)$ $5 \text{ unit}$ |
| $(B)$ Component along vector $(2 \hat{i} + \hat{j} + 2 \hat{k})$ | $(q)$ $4 \text{ unit}$ |
| $(C)$ Component along $(6 \hat{i} + 8 \hat{j} - 10 \hat{k})$ | $(r)$ $0$ |
| $(D)$ Component along $(-3 \hat{i} - 4 \hat{j} + 5 \hat{k})$ | $(s)$ None |
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