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Angle between two lines given in symmetric or parametric form

This type of question, asked 6 times: 13 May 2024 S2, 20 Apr 2025 S1, 21 Apr 2025 S2, 22 Apr 2025 S1, 17 Apr 2026 S1, 18 Apr 2026 S2. All 6 questions below, oldest first.

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  1. Question 1

    13 May 2024 S2

    104
    The acute angle between the line joining the points (2,1,−3)(2,1,-3), (−3,1,7)(-3,1,7) and a line parallel to x−13=y4=z+35\frac{x-1}{3}=\frac{y}{4}=\frac{z+3}{5} through the point (−1,0,4)(-1,0,4) is

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  2. Question 2

    20 Apr 2025 S1

    110
    The acute angle between the lines x=−2+2t,y=3−4t,z=−4+tx= - 2 + 2t,y= 3 - 4t,z = - 4 + t and x=−2−t,y=3+2t,z=−4+3tx= - 2 - t,y= 3 + 2t,z = - 4 + 3t is

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  3. Question 3

    21 Apr 2025 S2

    127
    The angle between the lines whose direction cosines are −34,14,−32\frac{-\sqrt{3}}{4},\frac{1}{4},\frac{-\sqrt{3}}{2} and −34,14,32\frac{-\sqrt{3}}{4},\frac{1}{4},\frac{\sqrt{3}}{2} is

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  4. Question 4

    22 Apr 2025 S1

    117
    The angle between the lines 3x=2y=−z3x= 2y= -z and −x=6y=−4z-x= 6y= - 4z is

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  5. Question 5

    17 Apr 2026 S1

    93
    If θ\theta is the angle between the lines x−12=2y+34; z=−2\dfrac{x - 1}{2} = \dfrac{2y + 3}{4};\ z = -2 and x=1; y−12=z+12x = 1;\ \dfrac{y - 1}{2} = \dfrac{z + 1}{2}, then

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  6. Question 6

    18 Apr 2026 S2

    96
    The acute angle between the lines 2x=3y=−z2x = 3y = -z and 6x=−y=−4z6x = -y = -4z is …\ldots

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