Question:
The equation of a plane containing the lines \( \vec{r} = (i + 2j - 4k) + \lambda (2i + 3j + 6k) \) and \( \vec{r} = (i + 3j + 4k) + \mu (i + j - k) \) is
The equation of a plane containing the lines \( \vec{r} = (i + 2j - 4k) + \lambda (2i + 3j + 6k) \) and \( \vec{r} = (i + 3j + 4k) + \mu (i + j - k) \) is
Show Hint
For planes containing two lines, use the cross product of their direction ratios to form the equation of the plane.
Updated On: Jan 26, 2026
- \( 9x + 8y + z + 11 = 0 \)
- \( 9x - 8y - z - 11 = 0 \)
- \( 9x - 8y - z + 11 = 0 \)
- \( 9x + 8y + z - 11 = 0 \)
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Find the direction ratios of the two lines.
The direction ratios for the first line are \( (2, 3, 6) \), and for the second line are \( (1, 1, -1) \).
Step 2: Use the vector equation of the plane.
The equation of the plane containing two lines is given by the cross product of their direction ratios. After calculation, we get the equation: \[ 9x + 8y + z - 11 = 0 \]
Step 3: Conclusion.
The correct answer is (D) \( 9x + 8y + z - 11 = 0 \).
The direction ratios for the first line are \( (2, 3, 6) \), and for the second line are \( (1, 1, -1) \).
Step 2: Use the vector equation of the plane.
The equation of the plane containing two lines is given by the cross product of their direction ratios. After calculation, we get the equation: \[ 9x + 8y + z - 11 = 0 \]
Step 3: Conclusion.
The correct answer is (D) \( 9x + 8y + z - 11 = 0 \).
Was this answer helpful?
0
0
Top Questions on Vector Algebra
- Let \(\overrightarrow{AB}=3\hat{i}+\hat{j}-\hat{k}\) and \(\overrightarrow{AC}=\hat{i}-\hat{j}+3\hat{k}\). If \(P\) is the point on the bisector of angle between \(\overrightarrow{AB}\) and \(\overrightarrow{AC}\) such that \(|\overrightarrow{AP}|=\dfrac{\sqrt{5}}{2}\), then the area of \(\triangle APB\) is:
- JEE Main - 2026
- Mathematics
- Vector Algebra
- If $2(\vec a \times \vec c)+3(\vec b \times \vec c)=0$, where $\vec a=2\hat i-5\hat j+5\hat k$, $\vec b=\hat i-\hat j+3\hat k$ and $(\vec a-\vec b)\cdot\vec c=-97$, find $|\vec c \times \vec k|^2$.
- JEE Main - 2026
- Mathematics
- Vector Algebra
- For given vectors \( \mathbf{a} = -\hat{i} + \hat{j} + 2\hat{k} \) and \( \mathbf{b} = 2\hat{i} - \hat{j} + \hat{k} \), where \( \mathbf{c} = \mathbf{a} \times \mathbf{b} \) and \( \mathbf{d} = \mathbf{c} \times \mathbf{b} \), then the value of \( (\mathbf{a} - \mathbf{b}) \cdot \mathbf{d} \) is:
- JEE Main - 2026
- Mathematics
- Vector Algebra
- For given vectors \( \vec{a} = -\hat{i} + \hat{j} + 2\hat{k} \) and \( \vec{b} = 2\hat{i} - \hat{j} + \hat{k} \) where \( \vec{c} = \vec{a} \times \vec{b} \) and \( \vec{d} = \vec{c} \times \vec{b} \). Then the value of \( (\vec{a}-\vec{b}) \cdot \vec{d} \) is:
- JEE Main - 2026
- Mathematics
- Vector Algebra
- If three vectors are given as shown. If the angle between vectors \( \mathbf{p} \) and \( \mathbf{q} \) is \( \theta \) where \( \cos \theta = \frac{1}{\sqrt{3}} \), \( |\mathbf{p}| = 2 \), and \( |\mathbf{q}| = 2 \), then the value of \( |\mathbf{p} \times (\mathbf{q} - 3\mathbf{r})|^2 - 3|\mathbf{r}|^2 \) is:
- JEE Main - 2026
- Mathematics
- Vector Algebra
View More Questions
Questions Asked in MHT CET exam
- If $ f(x) = 2x^2 - 3x + 5 $, find $ f(3) $.
- MHT CET - 2025
- Functions
- Evaluate the definite integral: \( \int_{-2}^{2} |x^2 - x - 2| \, dx \)
- MHT CET - 2025
- Definite Integral
- There are 6 boys and 4 girls. Arrange their seating arrangement on a round table such that 2 boys and 1 girl can't sit together.
- MHT CET - 2025
- permutations and combinations
- Given the equation: \[ 81 \sin^2 x + 81 \cos^2 x = 30 \] Find the value of \( x \).
- MHT CET - 2025
- Trigonometric Identities
- Evaluate the integral: \[ \int \frac{1}{\sin^2 2x \cdot \cos^2 2x} \, dx \]
- MHT CET - 2025
- Trigonometric Identities
View More Questions