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If a line makes angle pi/3\ a n d\ pi/4 ...

If a line makes angle `pi/3\ a n d\ pi/4` with x-axis and y-axis respectively, then the angle made by the line with z-axis is `pi//2` b. `pi//3` c. `pi//4` d. `5pi//12`

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To find the angle made by the line with the z-axis, we can use the relationship between the angles a line makes with the three coordinate axes (x, y, and z). The angles made with the axes are denoted as α (with the x-axis), β (with the y-axis), and γ (with the z-axis). 1. **Given Angles:** - The angle with the x-axis, α = π/3 - The angle with the y-axis, β = π/4 2. **Using the Relationship:** The relationship between the angles is given by the equation: ...
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Knowledge Check

  • If a line makes angle (pi)/3 and (pi)/4 with x-axis and y-axis respectively then the angle made by the line with z-axis, is

    A
    `(pi)/2`
    B
    `(pi)/3`
    C
    `(pi)/4`
    D
    `(5pi)/12`

  • If a line makes angles (pi)/(3) and (pi)/(4) with X-axis and Y-axis respectively, then the angle made by the line with Z-axis is

    A
    `(pi)/(2)`
    B
    `(pi)/(3)`
    C
    `(pi)/(4)`
    D
    `(5pi)/(12)`

  • If a line makes angles (pi)/(2), (3pi)/(4) and (pi)/(4) with x,y,z axis respectively, then direction cosines of this line are :

    A
    `pm` (1,1,1)
    B
    `pm (0, (1)/(sqrt(2)), (1)/(sqrt(2)))`
    C
    `pm ((1)/(2), (1)/(2), (1)/(2))`
    D
    `pm (0, -(1)/(sqrt(2)), (1)/(sqrt(2)))`

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