Given vectors a (1; 4) and b (-3; n). At what value of n these vectors will be perpendicular.

We will use the fact that two vectors will be perpendicular if and only if their dot product is 0.

According to the condition of the problem, vector a has coordinates (1; 4), vector b has coordinates (-3; n) and the scalar product of these vectors is:

(a, b) = 1 * (-3) + 4 * n = 4n – 3.

Equating the expression 4n – 3 to zero, we can form the following equation:

4n – 3 = 0,

solving which, we get:

4n – 3 + 3 = 0 + 3;

4n = 3;

4n / 4 = 3/4;

n = 3/4 = 0.75.

Answer: vectors will be perpendicular at n = 0.75.