# If the planes #x=cy+bz# , #y=cx+az# , #z=bx+ay# go through the straight line, then is it true that #a^2+b^2+c^2+2abc=1#?

Yes, it is true. Please see below for details.

and substituting in third we get

By signing up, you agree to our Terms of Service and Privacy Policy

Yes, it is true. If the planes (x = cy + bz), (y = cx + az), and (z = bx + ay) go through the same straight line, then it follows that (a^2 + b^2 + c^2 + 2abc = 1). This relationship arises from the condition that the three planes intersect along a common line.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Circle A has a center at #(3 ,7 )# and a radius of #2 #. Circle B has a center at #(1 ,3 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?
- A triangle has corners at #(1 ,6 )#, #(8 ,2 )#, and #(5 ,9 )#. How far is the triangle's centroid from the origin?
- What is the perimeter of a triangle with corners at #(6 ,4 )#, #(8 ,2 )#, and #(4 ,7 )#?
- Is my teacher's final answer wrong?
- If #P(x,y)# lies on the interval #A(x_1,y_1), B(x_2,y_2)# such that #AP : PB =a : b#, with a and b positive, show that #x= (bx_1+ax_2) /(b+a)# and #y=(by_1+ay_2)/(b+a)#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7