[tex](adsbygoogle = window.adsbygoogle || []).push({});

T(x,y,z) = x^2 - y^2 + z^2 + xz^2

[/tex]

[tex]

3x^2 - y^2 - z = 0

[/tex]

[tex]

2x^2 + 2y^2 - z^2 = 0

[/tex]

[tex]

\bigtriangledown T (x,y,z) = (2x + z^2, -2y, 2z(1+x))

[/tex]

[tex]

\bigtriangledown T (1,1,2) = 2(3, -1, 4)

[/tex]

[tex]

D_{\overrightarrow{v}}(1,1,2) = \bigtriangledown T(1,1,2).\overrightarrow{v} = 2(3v_1 - v_2 + 4v_3)

[/tex]

[tex]

T_1 = (6x, -2y, -1)

[/tex]

[tex]

T_2 = (4x, 4y, -2z)

[/tex]

[tex]

T_1 = (6, -2, -1)

[/tex]

[tex]

T_2 = (4, 4, -4)

[/tex]

[tex]

\overrightarrow{n} = T_1\ \mbox{x}\ T_2 = (12, 20, 32) = 4(3,5,8)

[/tex]

[tex]

||\overrightarrow{n}|| = 4\sqrt{9 + 25 + 64} = 28\sqrt{2}

[/tex]

[tex]

\frac{2.7.4}{28\sqrt{2}} (3.3 - 5 + 4.8) = 33\sqrt{2} \frac{°C}{s}

[/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Flea problem

**Physics Forums | Science Articles, Homework Help, Discussion**