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In space, points of the form $(x, y, 0)$ lie in a plane called the____.
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The x-axis represents the horizontal direction, the y-axis represents the vertical direction, and the z-axis represents the depth direction. Show more…
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In space, points of the form $(x, y, 0)$ lie in a plane called the ___________.
Find a condition for four points in space to lie in a plane. Your answer should be in the form of a determinant which must be equal to zero. Hint: The equation of a plane is of the form $a x+b y+c z=d$, where $a, b, c, d$ are constants. The four points $\left(x_{1}, y_{1}, z_{1}\right)$ $\left(x_{2}, y_{2}, z_{2}\right)$, etc., are all to satisfy this equation. When can you find $a, b, c, d$ not all zero?
LINEAR EQUATIONS; VECTORS, MATRICES, AND DETERMINANTS
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Fill in the blanks: (i) The $x$ -axis and $y$ -axis taken together determine a plane known as (ii) The coordinates of points in the XY-plane are of the form (iii) Coordinate planes divide the space into octants.
Introduction to Three Dimensional Geometry
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