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If there are two vectors \(\vec A\) and \(\vec B\) such that \(2\vec A+\vec B=\hat i+\hat j+\hat k\) and \(\vec A-\vec B=\hat i-\hat k\), then choose the correct option.

1. The angle between \(\vec A\) and \(\vec B\) is 60°
2. \(\vec A=\hat i+\hat j\)
3. \(\vec B=\hat j+\hat k\)
4. The angle between \(\vec A\) and \(\vec B\) is 120°

Correct answer: \(\vec B=\hat j+\hat k\)

Solution

From \(2\vec A+\vec B=\hat i+\hat j+\hat k\) and \(\vec A-\vec B=\hat i-\hat k\), solve simultaneously to get the vectors. The solution gives \(\vec B=\hat j+\hat k\), which matches one option.

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