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Line and Plane — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsLine and Plane2 Marks
MCQ
If the line $\overline{ r }=\hat{ i }+\lambda(2 \hat{ i }- m \hat{ j }-3 \hat{ k })$ is parallel to the plane $\overline{ r } \cdot( m \hat{ i }+3 \hat{ j }+\hat{ k })=0$, then m is equal to
  • A
    3
  • ✓
    -3
  • C
    1
  • D
    -1
✓

Answer

Correct option: B.
-3
(B)
Since the line $\bar{r}=\hat{i}+\lambda(2 \hat{i}-m \hat{j}-3 \hat{k})$ is parallel to the plane $\overline{ r } \cdot( m \hat{ i }+3 \hat{ j }+\hat{ k })=0$
$\therefore \quad \overline{ b } \cdot \overline{ n }=0$
$\Rightarrow(2 \hat{i}-m \hat{j}-3 \hat{k}) \cdot(m \hat{i}+3 \hat{j}+\hat{k})=0$
$\Rightarrow 2(m)- m (3)-3(1)=0$
$\Rightarrow-m=3$
$\Rightarrow m =-3$

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