List of top Mathematics Questions on Plane asked in KEAM

The equation of the plane containing the lines \[ \frac{x+1}{3} = \frac{y+3}{5} = \frac{z+5}{7} \text{and} \frac{x-2}{2} = \frac{y-4}{3} = \frac{z-6}{5} \]

A plane passes through the point \( (1,-2,1) \) and is perpendicular to planes \(2x-2y+z=0\) and \(x-y+2z=4\). Then the equation of the plane is

The equation of the plane containing the line \( \frac{x-\alpha}{l} = \frac{y-\beta}{m} = \frac{z-\gamma}{n} \) is \( a(x-\alpha)+b(y-\beta)+c(z-\gamma)=0 \), where \( al + bm + cn \) is equal to

Find plane at distance 5 from origin perpendicular to \(2\hat{i}+\hat{j}+2\hat{k}\)

Find equation of plane passing through (1,2,3), (-1,4,2), (3,1,1)

Find plane at distance 5 from origin perpendicular to \(2\hat{i}+\hat{j}+2\hat{k}\)

The equation of the plane that passes through the points \( (1, 0, 2), (-1, 1, 2) \) and \( (5, 0, 3) \) is:

The equation of the plane passing through $(-1, 5, -7)$ and parallel to the plane $2x - 5y + 7z + 11 = 0$, is:

The plane \( x+3y+13=0 \) passes through the line of intersection of the planes \( 2x-8y+4z=p \) and \( 3x-5y+4z+10=0 \). If the plane is perpendicular to the plane \( 3x-y-2z-4=0 \), then the value of \( p \) is equal to

The equation of the plane which bisects the line segment joining the points \( (3,2,6) \) and \( (5,4,8) \) and is perpendicular to the same line segment, is

The angle between the straight lines \( x - 1 = \frac{2y + 3}{3} = \frac{z + 5}{2} \) and \( x = 3r + 2; y = -2r - 1; z = 2 \), where \( r \) is a parameter, is:

The angle between the straight lines \( x - 1 = \frac{2y + 3}{3} = \frac{z + 5}{2} \) and \( x = 3r + 2; y = -2r - 1; z = 2 \), where \( r \) is a parameter, is:

The angle between the straight lines \( x - 1 = \frac{2y + 3}{3} = \frac{z + 5}{2} \) and \( x = 3r + 2; y = -2r - 1; z = 2 \), where \( r \) is a parameter, is: