No. A line can lie in many planes. A plane can be defined by three non-linear points. Since a line is defined by only two points, we need another point. (Note that point C alone, or line AB alone belong to an infinite number of planes.)
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Yes, a line lies in only one plane. This is a fundamental property of geometry where a line can be uniquely defined by two points and can only exist within a single plane.
A line has one dimension. You can figure out how many dimensions a shape has by asking yourself how many coordinates you need to find a point within that shape. The points on a line can be described by just one number each, so it has one dimension. The points on a plane need two numbers to describe them (x and y coordinates), so a plane has two dimensions.
All planets lie in the plane of their orbit, but most spin on an that is nearly (many have tilted axes of spin) perpendicular to that plane. The one exception is the planet Uranus which has its axis of spin lying very close to its orbital plane.
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There is only one midsagittal plane through your body. It divides the body into equal left and right portions.
An animal with bilateral symmetry is divided by one line into two equal halves. This line is called the sagittal plane.