Question

The distance between the parallel planes ax+by+cz+d1=0 and ax+by+cz+d2=0 is:

a) ( ((|d2 - d1|))/((√(a² + b² + c²))) )
b) ( ((|d1 - d2|))/((√(a² + b² + c²))) )
c) ( ((|d2 - d1|))/((a² + b² + c²)) )
d) ( ((|d1 - d2|))/((a² + b² + c²)) )

Answer 1

The distance between two parallel planes is determined by the formula (|d1 - d2|)/(\u221A(a² + b² + c²)), taking the absolute value of the difference between 'd1' and 'd2', and dividing by the magnitude of the normal to the planes.

Step-by-step explanation:

The distance between the parallel planes ax+by+cz+d1=0 and ax+by+cz+d2=0 is given by the formula: (|d2 - d1|)/(\u221A(a² + b² + c²)).

To calculate this distance, the difference between the two 'd' values is taken to account for the separation along the normal to the planes, and then this difference is divided by the magnitude of the normal vector, which is calculated using the square root of the sum of the squares of the coefficients of x, y, and z. Therefore, the correct answer to the question is b) ((|d1 - d2|)/((\u221A(a² + b² + c²)))).