Doubt from magnetism

How is net direction of magnetic field is obtained like in illustration 15 iiird case 2 are out of page and one into the page then how it is decided that final B will be into the page

See magnitude
The one which has highest magnitude will dominate direction here as (angle b/w all vectors here is 0,π)

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For question 2 i am getting different answer from what given in answer key.

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I also getting similar expression as you but without π

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Yes thank you for telling there will be no pi in final i just noticed one mistake.

Question 12 i am stuck at this integration what to substitute to find integration to get magnetic field.

Substitute r=x tan theta