Login/Sign Up
Home » Find the value of m for which the line is parallel to the plane
Find the value of m for which the line \overrightarrow r = (\widehat i + 2\widehat k) + \lambda (2\widehat i - m\widehat j - 3\widehat k) is parallel to the plane \overrightarrow r .(m\widehat i + 3\widehat j + \widehat k) = 4
CBSE | Class 12 | Exercise 28G | Maths | RS Aggarwal | The Planes
Find the value of m for which the line \overrightarrow r = (\widehat i + 2\widehat k) + \lambda (2\widehat i - m\widehat j - 3\widehat k) is parallel to the plane \overrightarrow r .(m\widehat i + 3\widehat j + \widehat k) = 4

Answer:

Given equation of line,

\overrightarrow r = (\widehat i + 2\widehat k) + \lambda (2\widehat i - m\widehat j - 3\widehat k)

Comparing with the line \overrightarrow r = \overrightarrow a + \lambda \overrightarrow b,

\overrightarrow a = \widehat i + 2\widehat k

\overrightarrow b = 2\widehat i - m\widehat j - 3\widehat k

Comparing with \vec{r} \cdot \vec{n}=d \Rightarrow \vec{n}=(m \hat{i}+3 \hat{j}+\hat{k})

Since the line is paralle! to the plane

⇒b→·n→=0⇒(2i^–mj^–3k^)·(mi^+3j^+k^)=0⇒2m–3m–3=0⇒–m–3=0⇒m=–3

\begin{array}{l}

\Rightarrow \vec{b} \cdot \vec{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-3 m-3=0 \\

\Rightarrow-m-3=0 \\

\Rightarrow m=-3

\end{array}

 

i

More Material