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Three Dimensional Geometry — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsThree Dimensional Geometry1 Mark
Question
The angle made by line $\text{r}[\cos\theta−3​\sin\theta]=5 $ with initial line is:
  1. 30°
  2. 45°
  3. 60°
  4. 90°
✓

Answer

  1. 30°

Solution:

Given equation

$\text{r}[\cos\theta−3​\sin\theta]=5 $

$\text{x}−\sqrt{3}\text{​y}=5$

Slope of the line is $\tan\theta=\frac{1}{\sqrt{3}}​$

$\Rightarrow\theta=30^\circ$

Hence, the line makes an angle of 30° with the initial line.

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