Find the unit vector perpendicular to the surface x² + y² – z² = 11 at the point (4, 2, 3).

Given:

Surface is x2 + y2 – z2 = 11

At point (4, 2, 3)

Formula used:

Unit vector perpendicular to the surface at point 'n' given by \(\frac{\hat{n}}{\hat{|n|}}\)

Calculation:

\({\hat{|n|}} = \sqrt{4^2 + 2^2 + (-3)^2} = \sqrt{29}\)

∴ The unit vector perpendicular to the surface x2 + y2 – z2 = 11 at the point (4, 2, 3) = \(\frac{{4\widehat i + 2\widehat j - 3\widehat k}}{{\sqrt {29} }}\)