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

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Answer 2

`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
`13`.

`√(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`.

`√(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`