The magnitude of the vector a = (5, m) is 13, and the magnitude of the vector b = (n, 24) is 25. What are m and n

Question

The magnitude of the vector a = (5, m) is 13, and the

magnitude of the vector b = (n, 24) is 25. What are m and

n

Answer 1

The first thing to know is that the formula for magnitude of a vector (x, y) is this: √(x²+y²)

So for vector a, that'll be √(5²+m²) = 13, or √(25+m²) = 13

And for vector b, it'll be √(n²+24²) = 25, or √(n²+576) = 25

Then what I would do for each one is square both sides to solve for the variable, so

Vector a: 25 + m² = 169

m² = 144

m = 12

Vector b: n² + 576 = 625

n² = 49

n = 7

You might also notice that these make up the Pythagorean triples (5, 12, 13) and (7, 24, 25)!