Ok, so I figure a load of you are good at mathematics, so maybe you can help me with what seems to be a really simple question but has me totally stumped.
Consider two vectors R and r such that R >> r. Show that in the first order in a small parameter r/R,
1 / |R - r| = 1 / sqrt(R^2 - R.r + r^2)
is approximately
1/R + (R . r) / R^3
Now, the first step (going to the square root) is just evaluating the length of the vector |R - r| so that makes sense, but the next step is the Taylor expansion which I totally don't understand. How do I take the Taylor expansion of a vector, or even two vectors? Can anyone help?
Consider two vectors R and r such that R >> r. Show that in the first order in a small parameter r/R,
1 / |R - r| = 1 / sqrt(R^2 - R.r + r^2)
is approximately
1/R + (R . r) / R^3
Now, the first step (going to the square root) is just evaluating the length of the vector |R - r| so that makes sense, but the next step is the Taylor expansion which I totally don't understand. How do I take the Taylor expansion of a vector, or even two vectors? Can anyone help?
"The trouble with the world is that the stupid are cocksure and the intelligent are full of doubt. " - Bertrand Russell
The Triumph of Stupidity in Mortals and Others 1931-1935
The Triumph of Stupidity in Mortals and Others 1931-1935