Project ForgeEngineering Mathematics
Linear Algebra
GATE 2019
Medium
The position vector of point P(20,10) is rotated anti-clockwise in the X-Y plane by an angle θ=30° such that P occupies position Q. The coordinates (x,y) of Q are
- A(13.40, 22.32)
- B(22.32, 8.26)
- (12.32, 18.66)
- D(18.66, 12.32)
Explanation
For a 30° anticlockwise rotation: x' = x cosθ − y sinθ = 20(0.866) − 10(0.5) = 17.32 − 5 = 12.32. y' = x sinθ + y cosθ = 20(0.5) + 10(0.866) = 10 + 8.66 = 18.66.
Source: GATE ME 2019 Session 1 (Set 1) (2019)
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