(4A-4)
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Recall that the plane shaded in pink has the equation
z = -x - 2y
The line shown in white is x=y, in the plane z=0.
The line shown in yellow is the line in the pink plane which points in the direction x = y
In this exercise lets use (x,y) coordinates. So, point 0 is the origin, (0,0). Point A is (0,-2) and point B is (-2,-2).
① What is the distance 0B ?
② Point C is the point on the pink plane where x = y = -2. What is the distance BC?
③ What, therefore, is the gradient of the yellow line, which is the slope of the plane z = -x - 2y, in the direction x = y ?
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