Download App

Line and Plane — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsLine and Plane2 Marks
MCQ
The angle between the line $\bar{r}=(2 \hat{i}+3 \hat{j}+\hat{k})+\lambda(\hat{i}+2 \hat{j}-\hat{k})$ and the plane $\bar{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=4$ is
  • A
    $\sin ^{-1}\left(\frac{1}{3}\right)$
  • ✓
    $\sin ^{-1}\left(\frac{1}{6}\right)$
  • C
    $\frac{\pi}{3}$
  • D
    $\frac{\pi}{4}$
✓

Answer

Correct option: B.
$\sin ^{-1}\left(\frac{1}{6}\right)$
(B)
Comparing the equations of line and plane with $\overline{ r }=\overline{ a }+\lambda \overline{ b }$ and $\overline{ r } . \overline{ n }= p$, we get $\bar{b}=\hat{i}+2 \hat{j}-\hat{k}$ and $\bar{n}=2 \hat{i}-\hat{j}+\hat{k}$
∴ The angle between the line and plane is
$\sin \theta=\left|\frac{\overline{ b } \cdot \overline{ n }}{|\overline{ b }| \cdot|\overline{ n }|}\right|=\left|\frac{1(2)+2(-1)-1(1)}{\sqrt{1+4+1} \sqrt{4+1+1}}\right|=\frac{1}{6}$
$\Rightarrow \theta=\sin ^{-1}\left(\frac{1}{6}\right)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Line and Plane→Line and Plane — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

The projection of the vector $\hat{i}-2 \hat{j}+\hat{k}$ on the vector $4 \hat{i}-4 \hat{j}+7 \hat{k}$ is
→
Equation of a line passing through the point with position vector $2 \hat{i}-3 \hat{j}+4 \hat{k}$ and in the direction of the vector $3 \hat{i}+4 \hat{j}-5 \hat{k}$ is
→
$\int_0^1 e ^{2 \log x} dx =$
→
If in a triangle the angles are in A. P. and $b: c=\sqrt{3}: \sqrt{2}$, then $\angle A$ is equal to
→
If $\bar{a} \cdot \bar{b}=|\bar{a}||\bar{b}|$, then $\bar{a}$ and $\bar{b}$ are
→
Let p be the proposition : Mathematics is interesting and let q be the proposition : Mathematics is difficult, then the symbol p^q means
→
Let POR be a triangle of area $\Delta$ with $a =2$, $b =\frac{7}{2}$ and $c =\frac{5}{2}$, where $a, b$ and $c$ are the lenghts of the sides of the triangle opposite to the angles at $P, Q$ and $R$ respectively. Then $\frac{2 \sin P-\sin 2 P}{2 \sin P+\sin 2 P}$ equals
→
The determinant $\begin{vmatrix}\text{b}^2-\text{ab}&\text{b}-\text{c}&\text{bc}-\text{ac}\\\text{ab}-\text{a}^2&\text{a}-\text{b}&\text{b}^2-\text{ab}\\\text{bc}-\text{ac}&\text{c}-\text{a}&\text{ab}-\text{a}^2\end{vmatrix}$ equals:
→
If $\bar{a}=\hat{i}+2 \hat{j}-3 \hat{k}$ and $\bar{b}=3 \hat{i}-\hat{j}+2 \hat{k}$, then the angle between the vectors $\bar{a}+\bar{b}$ and $\bar{a}-\bar{b}$ is
→
Area bounded by the parabola $y^2=4 ax$ and its latus rectum is
→