Find the angle between the vectors with direction ratios proportional to `4,-3,5` and `3,4,5.`

Explanation

`3 hat{i}+4 hat{j}+5 hat{k}=vec{a} `
`
4 hat{i}-3 hat{j}+5 hat{k}=vec{b} `
`
cos theta=frac{vec{a} cdot vec{b}}{|vec{a}||vec{b}|} `
`
cos theta=frac{(3 hat{i}+4 hat{j}+5 hat{k}) cdot(hat{4 i}-3 hat{j}+5 hat{k})}{sqrt{9+16+25} sqrt{9+16+25}} `
`
cos theta=(frac{25}{50}) `
`
theta=(frac{pi}{3})`

The angle between the lines in`(frac{pi}{3})`