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Acute angle between two given lines

This type of question, asked 3 times: 4 May 2023 S2, 20 Apr 2025 S1, 26 Apr 2025 S2. All 3 questions below, oldest first.

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  1. Question 1

    4 May 2023 S2

    147
    The acute angle between the lines xcos⁡30°+ysin⁡30°=3x\cos30°+y\sin30°=3 and xcos⁡60°+ysin⁡60°=5x\cos60°+y\sin60°=5 is

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  2. Question 2

    20 Apr 2025 S1

    104
    The acute angle between the diagonals of a parallelogram whose vertices are A(2,−1)A(2, - 1), B(0,2),C(2,3)B(0,2),C(2,3) and D(4,0)D(4,0) is

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  3. Question 3

    26 Apr 2025 S2

    104
    The acute angle between the line 4x−2y+13=04x- 2y+ 13 = 0 and the line which makes equal intercepts with the co-ordinate axes is

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