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(x)/(1)=y/1=(z)/(-1) " and " (x)/(3) ...

`(x)/(1)=y/1=(z)/(-1) " and " (x)/(3) =(y)/(4)=(z)/(5)` Find the angle between the lines .

Text Solution

Verified by Experts

The correct Answer is:
`cos^(-1) .((2)/(5sqrt6))`
Given lines in standard form are :
`(x)/(1) =(y-0)/(0)=(z-1)/(-1) "and " (x)/(3)=(y)/(4)=(z)/(5)`
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(x+1)/(1)=(y-4)/(1)=(z-5)/(2) " and " (x+3)/(3) =(y-2)/(5)=(z+5)/(4) Find angle between the lines .

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Knowledge Check

  • If the lines (x-2)/(1)=(y-3)/(1)=(z-4)/(lamda) and (x-1)/(lamda)=(y-4)/(2)=(z-5)/(1) intersect then

    A
    `lamda=-1`
    B
    `lamda=2`
    C
    `lamda=-3`
    D
    `lamda=0`

  • The angle between the lines (x)/(1)=(y)/(0)=(z)/(-1)and(x)/(3)=(y)/(4)=(z)/(5) is

    A
    `cos^(-1)((1)/(5))`
    B
    `cos^(-1)((1)/(3))`
    C
    `cos^(-1)((1)/(2))`
    D
    `cos^(-1)((1)/(4))`

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    Explore conceptually related problems

    (5-x)/(3) =(y+3)/(-2) ,z=5 " and " (x-1)/(1)=(1-y)/(3)=(z-5)/(2) Find the angle between the lines.

    (x-4)/(3) =(y+1)/(4) =(z-6)/(5) " and " (x-5)/(1)=(2y+5)/(-2) =(z-3)/(1) Find angle between the lines

    Find the equation of the line intersecting the lines (x-a)/(1)=(y)/(1)=(z-a)/(1) and (x+a)/(1)=(y)/(1)=(z+a)/(2) and parallel to the line (x-a)/(2)=(y-a)/(1)=(z-2a)/(3)

    Show that the lines (x-5)/(7) =(y+2)/(-5)=(z)/(1) " and " (x)/(1) =(y)/(2)=(z)/(3) are at right angles .

    (i) Find the angle between the line : (x + 1)/(2) = (y)/(3) = (z - 3)/(6) and the plane 10x + 12y - 11z = 3 (ii) Find the angle between the line : (x + 1)/(2) = (y -1)/(2) = (z -2)/(4) and the plane 2x + y - 3z + 4 =0 . (iii) Find the angle between the plane 2x + 4y - z = 8 and line (x - 1)/(2) = (2 - y)/(7) = (3z + 6)/(12) (iv) Find the angle between the line (x - 1)/(3) = (3 -y)/(-1) = (3z + 1)/(6) and the plane 3x - 5y + 2z = 10 .

    If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/(-2) and (x-1)/(3k)=(y-5)/(1)=(z-6)/(-5) are at right angle,then find the value of k

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