Show that the steady-state solutions to the diffusion equation in linear geometry, in planar geometry with radial symmetry, and in spatial geometry with spherical symmetry are, respectively,

4. Find the point of intersection (if any) of the line with parametric equations x = 1+2t, y = -1+t, and z = 2+3t and the plane 2x + 3y – 4z = 6* - u dod ot lenogo

1. Convert point P(2,3,-1) and vector A ya, xayt za, into cylindrical coordinates.

1) Three vectors a, b, and c are said to be coplanar if and only if a = mb + nc where m and n are scalars. Show that a = 2i +3j + k, b = i- j and c = 7i+ 3j+ 2k are coplanar by writing a as a linear combination of b and c. 2) Eliminate the parameter t to find the rectangular equation of the curve represented by the parametric equations x =√ and y=√1 And sketch the curve (indicate the direction of trace in increasing order of t). 3) Find a unit vector that is perpendicular to the plane containing the vectors a = (2, -6, -3) and b = (4, 3, -1) without using cross product.