Question

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

Answer 1

Answer:

$m=12\,,n=7$

Step-by-step explanation:

The magnitude of vector $(x,y)$ is given by $\sqrt{x^2+y^2}$

The magnitude of vector $a=(5,m)$ is $13$.

$\sqrt{5^2+m^2}=13\\5^2+m^2=13^2\\25+m^2=169\\m^2=169-25\\m^2=144\\m=12$

The magnitude of vector $b=(n,24)$ is $25$.

$\sqrt{n^2+24^2}=25\\n^2+24^2=25^2\\n^2+576=625\\n^2=625-576\\n^2=49\\n=7$

Therefore,

$m=12\,,n=7$