A description of a plane is given Find an equation for the p

A description of a plane is given. Find an equation for the plane. The plane that crosses the x-axis where x = 1, the y-axis where y = 2, and the z-axis where z = 5. ______________ A description of a plane is given. Find an equation for the plane. The plane that contains all the points that are equidistant from the points P(-5, -3, 0) and Q(3, -1, -4). _______________

Solution

Here the intercepts are given that is (1,0,0) ,(0,2,0),(0,0,5)

And equation of plane is ax+by +cz=d

plugging those three points in the equation of plane we get

a=d

2b=d

5c=d

To find the value of d,we have to take the lcm of 1,2 and 5 which is 10

Therefore d=10

a=d=10

2b=10

b=5

5c=10

c=2

Therefore equation of plane is 10x + 5y + 2z=10