- #1

songoku

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- 331

- Homework Statement
- Please see below

- Relevant Equations
- Partial Derivative

Direction derivative in the direction of unit vector u = <a, b, c>:

Du f(x,y,z) = fx (x,y,z) a + fy (x,y,z) b + fz (x, y, z)

I want to ask about the direction in which ##D_v## is zero at point (1, 2, 1)

My attempt:

$$w_x=yz+\frac{1}{x}$$

$$w_y=xz+\frac{1}{y}$$

$$w_z=xy+\frac{1}{z}$$

At point (1, 2, 1), the ##\nabla w=<3, \frac{3}{2}, 3>##

$$D_v w=0$$

$$\nabla w \cdot v=0$$

$$

\begin{pmatrix}

3 \\

\frac{3}{2} \\

3

\end{pmatrix}

\cdot

\begin{pmatrix}

p \\

q \\

r

\end{pmatrix}

=0

$$

$$3p+\frac{3}{2} q+3r=0$$

$$2p+q+2r=0$$

Another equation is ##p^2+q^2+r^2=1##

But I can't find ##p, q## and ##r## from these equations. Is my working wrong?

Thanks

Last edited: