Question

Obtain the directional derivative for a scalar field $(x,y,z) = 3x2y - yºz2 at the
point (1, -2, -1) in the direction i+i+k.​

Answer 1

Answer:

Let us consider A ( scalar) = 3x^2y + y^0z^2

= 3x^2y + z^2 , ( y^0 = 1 )

gradA = 6xy i + 3x^2 j + 2z k

( gradA ) at point (1, -2, -1) = -12 i + 3 j - 2 k

unit vector = ( i + j + k ) / sqrt{3}

in the direction i+i+k = ( -12 i + 3 j - 2 k ) × ( i + j + k ) / sqrt{3}

= -11/sqrt{3}

The directional derivative for a scalar field $(x,y,z) = 3x2y - yºz2 at the

he directional derivative for a scalar field $(x,y,z) = 3x2y - yºz2 at thepoint (1, -2, -1) in the direction i+i+k is -11/sqrt{3}