Correct Answer - Option 2 :
\(\sqrt{114}\)
Concept:
Let A(x1, y1, z1) and B(x2, y2, z2) be two point on a 3D plane then the distance between the points A and B is given by:\(\rm \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}}\).
Calculation:
Given: C(- 1, 4, 5) and D(7, - 1, 0) are two points in a 3D plane.
As we know that, the distance between the points A(x1, y1, z1) and B(x2, y2, z2) is given by: \(\rm \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}}\)
Let d be the distance between the points C and D.
\(\Rightarrow \rm d=\sqrt{(7+1)^{2}+(-1-4)^{2}+(0-5)^{2}}=\sqrt{64+25+25}=\sqrt{114}\)
Hence, the correct option is 2.
