At what value of a is the length of the vector AB equal to 2√5? Point coordinates: A (-1; 6; 2); In (3; a; 4).

Find the coordinates of the vector AB (subtract the coordinates of point A from the coordinates of point B):

AB = ((3 – (-1); (a – 6); (4 – 2)) = (4; (a – 6); 2).

Then its length will be:

| AB | = √ (4 ^ 2 + (a – 6) ^ 2 + 2 ^ 2) = √ (20 + (a – 6) ^ 2).

Equating it to the given one, we learn the equation for a:

√ (20 + (a – 6) ^ 2) = 2√5.

Squaring we get:

20 + (a – 6) ^ 2 = 20;

(a – 6) ^ 2 = 20 – 20 = 0;

a – 6 = 0;

a = 6.

Answer: the desired value of the parameter a is 6.