The Plane 2x − (1 + λ) Y + 3λZ = 0 Passes Through the Intersection of the Planes (A) 2x − Y = 0 and Y − 3z = 0 (B) 2x + 3z = 0 and Y = 0 (C) 2x − Y + 3z = 0 and Y − 3z = 0 (D) None of These - Mathematics

प्रश्न

The plane 2x − (1 + λ) y + 3λz = 0 passes through the intersection of the planes

पर्याय

2x − y = 0 and y − 3z = 0
2x + 3z = 0 and y = 0
2x − y + 3z = 0 and y − 3z = 0
None of these

MCQ

उत्तर

2x − y = 0 and y − 3z = 0

$The given plane is$

$2 x - (1 + λ) y + 3 λ z = 0$

$\Rightarrow (2 x - y) + λ (- y + 3 z) = 0$

$So, this plane passes through the intersection of the planes$

$2 x - y = 0 and - y + 3 z = 0$

$\Rightarrow 2 x - y = 0 and y - 3 z = 0$

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Equation of a Plane - Plane Passing Through the Intersection of Two Given Planes

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

Q 1 Q 23 Q 2

पाठ 29: The Plane - MCQ [पृष्ठ ८४]

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आरडी शर्मा Mathematics [English] Class 12

पाठ 29 The Plane
MCQ | Q 1 | पृष्ठ ८४

संबंधित प्रश्‍न

Find the equation of the plane through the intersection of the planes 3x – y + 2z – 4 = 0 and x + y + z – 2 = 0 and the point (2, 2, 1).

Find the vector equation of the plane passing through the intersection of the planes $\vec{r} . (2 \hat{i} + 2 \hat{j} - 3 \hat{k}) = 7, \vec{r} . (2 \hat{i} + 5 \hat{j} + 3 \hat{k}) = 9$ and through the point (2, 1, 3)

Find the equation of the plane which contains the line of intersection of the planes $\vec{r} r . (\hat{i} + 2 \hat{j} + 3 \hat{k}) - 4 = 0, \vec{r} . (2 \hat{i} + h t j - \hat{k}) + 5 = 0$ , and which is perpendicular to the plane $\vec{r} . (5 \hat{i} + 3 \hat{j} - 6 \hat{k}) + 8 = 0$ .

Find the coordinates of the point where the line $\frac{x - 2}{3} = \frac{y + 1}{4} = \frac{z - 2}{2}$ intersects the plane x − y + z − 5 = 0. Also, find the angle between the line and the plane.

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Find the distance of the point P(−1, −5, −10) from the point of intersection of the line joining the points A(2, −1, 2) and B(5, 3, 4) with the plane $x - y + z = 5$ .

Find the distance of the point P(3, 4, 4) from the point, where the line joining the points A(3, −4, −5) and B(2, −3, 1) intersects the plane 2x + y + z = 7.

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Find the vector equation of the plane passing through three points with position vectors $\hat{i} + \hat{j} - 2 \hat{k}, 2 \hat{i} - \hat{j} + \hat{k} and \hat{i} + 2 \hat{j} + \hat{k} .$ Also, find the coordinates of the point of intersection of this plane and the line $\vec{r} = 3 \hat{i} - \hat{j} - \hat{k} + λ (2 \hat{i} - 2 \hat{j} + \hat{k}) .$

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The Plane 2x − (1 + λ) Y + 3λZ = 0 Passes Through the Intersection of the Planes (A) 2x − Y = 0 and Y − 3z = 0 (B) 2x + 3z = 0 and Y = 0 (C) 2x − Y + 3z = 0 and Y − 3z = 0 (D) None of These - Mathematics

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The Plane 2x − (1 + λ) Y + 3λZ = 0 Passes Through the Intersection of the Planes (A) 2x − Y = 0 and Y − 3z = 0 (B) 2x + 3z = 0 and Y = 0 (C) 2x − Y + 3z = 0 and Y − 3z = 0 (D) None of These - Mathematics

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