Can a plane be parallel to an axis?

Can a plane be parallel to an axis?

There are many planes parallel to the x-axis, but the common property of all of them is that their normal vector lies in the yz-plane. Now consider that planes are defined to be orthogonal iff their normal vectors are, and you get the result.

What would the direction of the vector be if it is parallel to the x-axis?

We saw that the line is parallel to the 𝑥-axis. And so, it will never travel up or down. The direction vector will, therefore, be any multiple of the vector one, zero. One, zero is the simplest vector we can choose.

What is the implication if a linear graph is parallel to x-axis?

The slope of a straight line parallel to the x-axis will always be ‘0’ as there will be no slope to the straight line which is parallel to the axis.

What does it mean for a line to be parallel to a plane?

A line is parallel to a plane if the direction vector of the line is orthogonal to the normal vector of the plane. To check whether two vectors are orthogonal, you can find their dot product, because two vectors are orthogonal if and only if their dot product is zero.

What is the general equation of a plane parallel to Z axis?

bx+cz+d=0.

What is equation of plane parallel to x-axis?

The equation of plane is. ax+by+cz=1. Now the equation is parallel to x− axis, therefore coefficient of x will be zero.

Is YZ plane parallel to x-axis?

The plane parallel to yz-plane is perpendicular to x-axis.

Which graph is parallel to X?

Step-by-step explanation: Thus, if P(x, y) is any point on AB, then y = b. Hence, the equation of a straight line parallel to x-axis at a distance b from it is y = b. The equation of x-axis is y = 0, since, x-axis is a parallel to itself at a distance 0 from it.

What happens to the parallel lines?

Parallel lines never intersect. In the language of linear equations, this means that they have the same slope. In other words, for some change in the independent variable, each line will have identical change to each other in the dependent variable.

How do you know if planes are parallel?

Given two equations, A 1 x + B 1 y + C 1 z = D 1 and A 2 x + B 2 y + C 2 z = D 2 , the two planes are parallel when the ratios of each pair of coefficients are equal.

Is xy plane parallel to Z axis?

View of xy plane, z -axis is perpendicular to the sheet.