Question

Find the line through (3,1,2) that intersects and is perpendicular to the line:

a) The x-axis
b) The y-axis
c) The z-axis
d) The line x=y+z

Answer 1

To find the line through (3,1,2) that intersects and is perpendicular to different lines, we can use the concept of slope.

Step-by-step explanation:

To find the line through (3,1,2) that intersects and is perpendicular to different lines, we can use the concept of slope. Let's solve each part:

1. For the line parallel to the x-axis, the equation will be y = 1 and z = 2, as the y and z coordinates remain constant.

2. For the line parallel to the y-axis, the equation will be x = 3 and z = 2, as the x and z coordinates remain constant.

3. For the line parallel to the z-axis, the equation will be x = 3 and y = 1, as the x and y coordinates remain constant.

4. To find the line perpendicular to the line x = y + z, we need to find the slope of the given line and the negative reciprocal of the slope will give us the slope of the perpendicular line. The slope of x = y + z is 1, so the slope of the perpendicular line is -1. We can use the point-slope form of the equation and plug in the point (3,1,2) and the slope -1 to find the equation of the perpendicular line.