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Question: Answered & Verified by Expert
Let a vector $\bar{r}$ make angle $60^{\circ}, 30^{\circ}$ with $\mathrm{x}$ and y-axes respectively.
What are the direction cosines of $\bar{r}$ ?
MathematicsVector AlgebraNDANDA 2014 (Phase 1)
Options:
  • A $\left\langle\frac{1}{2}, \frac{\sqrt{3}}{2}, 0\right\rangle$
  • B $\left\langle\frac{1}{2}, \frac{\sqrt{3}}{2}, 0\right\rangle$
  • C $\left\langle\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0\right\rangle$
  • D $\left\langle-\frac{1}{2}, \frac{\sqrt{3}}{2}, 0\right\rangle$
Solution:
1375 Upvotes Verified Answer
The correct answer is: $\left\langle\frac{1}{2}, \frac{\sqrt{3}}{2}, 0\right\rangle$
$\left.\mathrm{r}= < 1, \mathrm{~m}, \mathrm{n}>; \mathrm{r}= < \cos 60^{\circ}, \cos 30^{\circ}, \cos 90^{\circ}\right\rangle$
Direction cosines of $\overrightarrow{\mathrm{r}}= < \frac{1}{2}, \frac{\sqrt{3}}{2}, 0>$

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