Mark against the correct answer in each of the following:
The equation of a plane through the point A(1, 0, -1) and perpendicular to the line is
A. 2x + 4y – 3z = 3
B. 2x – 4y + 3z = 5
C. 2x + 4y – 3z = 5
D. x + 3y + 7z = -6
Given: Plane passes through the point A(1, 0, -1).
Plane is perpendicular to the line
To find: Equation of the plane.
Formula Used: Equation of a plane is ax + by + cz = d where (a, b, c) are the direction ratios of the normal to the plane.
Let the equation of the plane be
ax + by + cz = d … (1)
Substituting point A,
a – z = d
Since the given line is perpendicular to the plane, it is the normal.
Direction ratios of line is 2, 4, -3
Therefore, 2 + 3 = d
d = 5
So the direction ratios of perpendicular to plane is 2, 4, -3 and d = 5
Substituting in (1),
2x + 4y – 3z = 5
Therefore, equation of plane is 2x + 4y – 3z = 5
Rate this question :
Find the equation of the plane which contains the line of intersection of the planes
and whose intercept on the x-axis is equal to that of on y-axis.Mathematics - Board Papers
Find the coordinates of the point where the line through the points A (3, 4, 1) and B (5, 1, 6) crosses the XY-plane.Mathematics - Board Papers
Find the distance of the point (–1, –5, –10), from the point of intersection of the line and the planeMathematics - Board Papers
Find the coordinates of the foot of the perpendicular and the perpendicular distance of the point P(3, 2, 1) from the plane 2x - y + z + 1 = 0. Find also, the image of the point in the plane.Mathematics - Board Papers
Find the Cartesian equation of the plane passing through the points A(0, 0, 0) and B(3, - 1, 2) and parallel to the lineMathematics - Board Papers