Saved Bookmarks
| 1. |
IF U=3x2y,V=xz2 -2y Evaluate [(grad U) (grad V)] |
|
Answer» U = 3x2y grad U = ∇ U = (i ∂/∂x + j ∂/∂y + k ∂/∂z) 3x2y = 6xy i + 3x2 j Also, V = xz2 - zy grad V = ∇ V = (i ∂/∂x + j ∂/∂y + k ∂/∂z) (xz2 - 2y) = z2 i - 2 j + 2xz k Now, (grad U).(grad V) = (6xy i + 3x2 j + 0 k) (z2 i - 2 j + 2xz k) = 6xyz2 + 6x2 = 6x (yz2 + x) |
|