Mathematics Crash Course MHT-CET>Chapter 25 - Plane>Exercise 1>Q 42

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IMPORTANT

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Equation of plane which contains the line $\frac{x - 1}{1} = \frac{y - 2}{3} = \frac{z - 3}{2}$ and which is perpendicular to the plane $2 x + 7 y + 5 z = 2,$ is

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Important Questions on Plane

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 25 - Plane>Exercise 1>Q 44

The vector equation of the plane passing through the intersection of the planes

\vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 1

and

\vec{r} \cdot (\hat{i} - 2 \hat{j}) = - 2,

and the point

(1, 0, 2)

is:

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Mathematics Crash Course MHT-CET>Chapter 25 - Plane>Exercise 1>Q 45

A plane is at a distance of

5

units from the origin and perpendicular to the vector

2 \hat{i} + \hat{j} + 2 \hat{k} .

The equation of the plane is

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Mathematics Crash Course MHT-CET>Chapter 25 - Plane>Exercise 1>Q 46

The vector equation of the plane through the point

2 \hat{i} - \hat{j} - 4 \hat{k}

and parallel to the plane

\vec{r} \cdot (4 \hat{i} - 12 \hat{j} - 3 \hat{k}) - 7 = 0

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Mathematics Crash Course MHT-CET>Chapter 25 - Plane>Exercise 1>Q 47

Equation of line of projection of the line $3 x - y + 2 z - 1 = 0 = x + 2 y - z - 2$ on the plane $3 x + 2 y + z = 0$ is

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Mathematics Crash Course MHT-CET>Chapter 25 - Plane>Exercise 1>Q 48

If planes

x - c y - b z = 0, c x - y + a z = 0

and

b x + a y - z = 0

pass through a straight line then

a^{2} + b^{2} + c^{2} =

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Mathematics Crash Course MHT-CET>Chapter 25 - Plane>Exercise 1>Q 49

The equation of the plane containing the line

2 x - 5 y + z = 3, x + y + 4 z = 5

and parallel to the plane

x + 3 y + 6 z = 1

is

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Mathematics Crash Course MHT-CET>Chapter 25 - Plane>Exercise 1>Q 50

The distance between the planes

x + 2 y + 3 z + 7 = 0

and

2 x + 4 y + 6 z + 7 = 0

is

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 25 - Plane>Exercise 1>Q 51

Equation of the plane passing through points

(1, 1, 1), (1, - 1, 1)

and

(- 7, - 3, - 5)

is