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

Question

asked May 26, 2022 47.4k views

2 Answers

Ecyshor · Answer 1 · 2022-05-31T07:48:39+0000

Answer:

$m=12\,,n=7$

Explanation:

The magnitude of vector
(x,y) is given by
√(x^2+y^2)

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

$√(5^2+m^2)=13\\5^2+m^2=13^2\\25+m^2=169\\m^2=169-25\\m^2=144\\m=12$

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

$√(n^2+24^2)=25\\n^2+24^2=25^2\\n^2+576=625\\n^2=625-576\\n^2=49\\n=7$

Therefore,

$m=12\,,n=7$