Choose correct alternatives : The equation of the plane in which the line `(x - 5)/(4) = (y - 7)/(4) = (z + 3)/(-5) and (x - 8)/(7) = (y - 4)/(1) = (z - 5)/(3)` lie, is

Choose correct alternatives : The equation of the plane in which the line andx-54=y-74=z+3-5andx-87=y-41=z-53 lie, is - Mathematics and Statistics

प्रश्न

Choose correct alternatives :

The equation of the plane in which the line $\frac{x - 5}{4} = \frac{y - 7}{4} = \frac{z + 3}{- 5} and \frac{x - 8}{7} = \frac{y - 4}{1} = \frac{z - 5}{3}$ lie, is

पर्याय

17x – 47y – 24z + 172 = 0
17x + 47y – 24z + 172 = 0
17x + 47y + 24z + 172 = 0
17x – 47y + 24z + 172 = 0

MCQ

उत्तर

17x – 47y – 24z + 172 = 0

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Equation of a Plane

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

Q 18 Q 17 Q 19

पाठ 6: Line and Plane - Miscellaneous Exercise 6 B [पृष्ठ २२५]

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board

पाठ 6 Line and Plane
Miscellaneous Exercise 6 B | Q 18 | पृष्ठ २२५

संबंधित प्रश्‍न

Find the length of the perpendicular (2, –3, 1) to the line $\frac{x + 1}{2} = \frac{y - 3}{3} = \frac{z + 1}{- 1}$ .

A(1, 0, 4), B(0, -11, 13), C(2, -3, 1) are three points and D is the foot of the perpendicular from A to BC. Find the co-ordinates of D.

Find the vector equation of a plane which is at 42 unit distance from the origin and which is normal to the vector $2 \hat{i} + \hat{j} - 2 \hat{k}$ .

Reduce the equation $\bar{r} . (3 \hat{i} + 4 \hat{j} + 12 \hat{k})$ to normal form and hence find
(i) the length of the perpendicular from the origin to the plane
(ii) direction cosines of the normal.

Find the vector equation of the plane passing through the point having position vector $\hat{i} + \hat{j} + \hat{k}$ and perpendicular to the vector $4 \hat{i} + 5 \hat{j} + 6 \hat{k}$ .

Choose correct alternatives :

If the line $\frac{x}{3} = \frac{y}{4}$ = z is perpendicular to the line $\frac{x - 1}{k} = \frac{y + 2}{3} = \frac{z - 3}{k - 1}$ , then the value of k is

Choose correct alternatives :

The lines $\frac{x}{1} = \frac{y}{2} = \frac{z}{3} and \frac{x - 1}{- 2} = \frac{y - 2}{- 4} = \frac{z - 3}{6}$ are

Solve the following :

Reduce the equation $\bar{r} . (6 \hat{i} + 8 \hat{j} + 24 \hat{k})$ = 13 normal form and hence find
(i) the length of the perpendicular from the origin to the plane.
(ii) direction cosines of the normal.

The equation of X axis is ______

Find direction cosines of the normal to the plane $\bar{r} \cdot (3 \hat{i} + 4 \hat{k})$ = 5

Find the vector equation of a plane at a distance 6 units from the origin and to which vector $2 \hat{i} - \hat{j} + 2 \hat{k}$ is normal

Show that the lines $\frac{x + 1}{- 10} = \frac{y + 3}{- 1} = \frac{z - 4}{1}$ and $\frac{x + 10}{- 1} = \frac{y + 1}{- 3} = \frac{z - 1}{4}$ intersect each other.also find the coordinates of the point of intersection

If z₁ and z₂ are z-coordinates of the points of trisection of the segment joining the points A (2, 1, 4), B (–1, 3, 6) then z₁ + z₂ = ______.

If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x + cos 3x + cos 4x = 0, is ______

The equation of the plane passing through the point (– 1, 2, 1) and perpendicular to the line joining the points (– 3, 1, 2) and (2, 3, 4) is ______.

Equation of the plane passing through A(-2, 2, 2), B(2, -2, -2) and perpendicular to x + 2y - 3z = 7 is ______

The equation of a plane containing the line of intersection of the planes 2x - y - 4 = 0 and y + 2z - 4 = 0 and passing through the point (1, 1, 0) is ______

The intercepts of the plane 3x - 4y + 6z = 48 on the co-ordinate axes are ______

Equations of planes parallel to the plane x - 2y + 2z + 4 = 0 which are at a distance of one unit from the point (1, 2, 3) are _______.

Equation of plane parallel to ZX-plane and passing through the point (0, 5, 0) is ______

If line $\frac{2 x - 4}{λ} = \frac{y - 1}{2} = \frac{z - 3}{1}$ and $\frac{x - 1}{1} = \frac{3 y - 1}{λ} = \frac{z - 2}{1}$ are perpendicular to each other then λ = ______.

The equation of the plane through (1, 2, -3) and (2, -2, 1) and parallel to the X-axis is ______

The distance of the point (1, 0, 2) from the point of intersection of the line $\frac{x - 2}{3} = \frac{y + 1}{4} = \frac{z - 2}{12}$ and the plane x - y + z = 16, is ______

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane 3y + 5 = 0.

Let the line $\frac{x - 2}{3} = \frac{y - 1}{- 5} = \frac{z + 2}{2}$ lie in the plane x + 3y - αz + β = 0. Then, (α, β) equals ______

The equation of the plane passing through a point having position vector $- 2 \hat{i} + 7 \hat{j} + 5 \hat{k}$ and parallel to the vectors $4 \hat{i} - \hat{j} + 3 \hat{k}$ and $\hat{i} + \hat{j} + \hat{k}$ is ______.

If the mirror image of the point (2, 4, 7) in the plane 3x – y + 4z = 2 is (a, b, c), then 2a + b + 2c is equal to ______.

Find the equation of the plane containing the lines $\frac{x - 1}{2} = \frac{y + 1}{- 1} = \frac{z}{3}$ and $\frac{x}{2} = \frac{y - 2}{- 1} = \frac{z + 1}{3}$ .

Reduce the equation $\bar{r} \cdot (3 \hat{i} - 4 \hat{j} + 12 \hat{k})$ = 3 to the normal form and hence find the length of perpendicular from the origin to the plane.

Find the equation of the plane which contains the line of intersection of the planes x + 2y + 4z = 4 and 2x – 3y – z = 9 and which is perpendicular to the plane 4x – 3y + 5z = 10.

Find the point of intersection of the line $\frac{x + 1}{2} = \frac{y - 1}{3} = \frac{z - 2}{1}$ with the plane x + 2y – z = 6.

A mobile tower is situated at the top of a hill. Consider the surface on which the tower stands as a plane having points A(1, 0, 2), B(3, –1, 1) and C(1, 2, 1) on it. The mobile tower is tied with three cables from the points A, B and C such that it stands vertically on the ground. The top of the tower is at point P(2, 3, 1) as shown in the figure below. The foot of the perpendicular from the point P on the plane is at the point $Q (\frac{43}{29}, \frac{77}{29}, \frac{9}{29})$ .

Answer the following questions.

Find the equation of the plane containing the points A, B and C.
Find the equation of the line PQ.
Calculate the height of the tower.

Find the equation of the plane containing the line $\frac{x}{- 2} = \frac{y - 1}{3} = \frac{1 - z}{1}$ and the point (–1, 0, 2).

Choose correct alternatives : The equation of the plane in which the line andx-54=y-74=z+3-5andx-87=y-41=z-53 lie, is - Mathematics and Statistics

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Choose correct alternatives : The equation of the plane in which the line andx-54=y-74=z+3-5andx-87=y-41=z-53 lie, is - Mathematics and Statistics

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