GATE 2019 AE – Question 12
Engineering Mathematics · Linear Algebra: Vector algebra, matrix algebra, systems of linear equations, rank, eigenvalues and eigenvectors · 1 mark · Multiple choice
Rotate the vector $\mathbf a=\mathbf i+\mathbf j$ through +90° about the k axis. The resulting vector is
- $\mathbf i-\mathbf j$
- $-\mathbf i+\mathbf j$
- $\mathbf i+\mathbf j$
- $-\mathbf i-\mathbf j$
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Show answer and explanation
Correct answer: (B) $-\mathbf i+\mathbf j$
Explanation
The positive rotation maps i to j and j to −i. Applying it to both components gives j−i, B. Equivalently, the planar rotation maps (1,1) to (−1,1).
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