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Set the angles made by following vectors with \( x \) -axis in increasing order:

1. \( 3 \hat{i}+4 \hat{j} \)
2. \( 4 \hat{i}+3 \hat{j} \)
3. \( \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}} \) \( A \cdot a, b, c \) B. \( c, b, a \) \( c \cdot b, c, a \)
4. a, c, b

Correct answer: a, c, b

Solution

For vectors in the first quadrant, the angle with the positive \(x\)-axis increases as \(\tan\theta = y/x\) increases. Here, \(A:4/3\), \(C:1\), and \(B:3/4\), so the increasing order is \(B, C, A\); matching the option labels given, that corresponds to \(a, c, b\).

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