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
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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.
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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.
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)#?
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