the acute angle in degrees that makes a with c, when a=4i+0j+k , c=i+j+3k

We need to find two things here, the dot product of the two vectors and the magnitude of each.

The dot product is <4, 0, 1 > (dot) < 1, 1, 3 > = (4 + 0 + 3) = 7

The magnitude of a = √(4² + 0² + 1²) =√(16 + 1) = √17

And the magnitude of c  = √(1² + 1² + 3²) =√(1 + 1 + 9) = √11

And the angle is given by

cos^-1 (a(dot)c / (llall * llcll)  = cos^-1 ((7) / (√17 * √11) = cos^-1 ((7) / (√187) = cos^-1 (0.5118906968889915) = about  59.2°