Problem 10
Question
Find the coordinates of the point. The point is located in the \(y z\) -plane, three units to the right of the \(x z\) -plane, and two units above the \(x y\) -plane.
Step-by-Step Solution
Verified Answer
The coordinates of the point are (3,0,2).
1Step 1: Identify the coordinates and their meaning in 3D space
In a three-dimensional Cartesian coordinate system, a point is defined by its position regarding the x, y, and z coordinates. Here, the point is in the yz-plane, so its x-coordinate is zero. This implies the point has moved right from the yz plane, giving us the x coordinate.
2Step 2: Determine the coordinates from the given conditions
If it is stated that the point is 'three units to the right' of the yz-plane, it means that the x-coordinate of the point is '3'. If it says 'two units above the xy-plane', it signifies that the z-coordinate of the point is '2'. The problem doesn't specify anything about the y-coordinate, so it's implied to be '0', since it's on the origin of the y-axis.
3Step 3: Write the coordinates of the point
The point having 'x-coordinate = 3', 'y-coordinate = 0' and 'z-coordinate = 2' is written as (3,0,2)
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