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Find the angle between the line (x-1)...

Find the angle between the line `(x-1)/3=(y-1)/2=(z-1)/4` and the plane `2x+y-3z+4=0.`

Text Solution

Verified by Experts

The angle between a line and a plane is complement of the angle between the line and the normal of the plane, i.e., 3, 2, 4 and normal 2, 1, -3. Therefore,
`" "costheta=(6+2-12)/(sqrt(29)*sqrt(14))=-(4)/(sqrt(406))`
`" "theta=cos^(-1) (-4//sqrt(406))`
`" "phi=90^(@)-theta`
`" " = 90^(@)- cos^(-1) * (-4//sqrt(406))`
`" " = sin ^(-1) (-4//sqrt(406))`
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Find the angle between the line (x-1)/3=(y+1)/2=(z-1)/4 and plane 2x + y - 3z + 4 = 0.

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Knowledge Check

  • The sine of the angle between the line (x-2)/(3) = (y-3)/(4) = (z-4)/(5) and the plane 2x-2y+z=5 is

    A
    `(10)/(6 sqrt5)`
    B
    `(4)/( 5 sqrt2)`
    C
    `(2 sqrt3)/(5)`
    D
    `( sqrt2)/(10)`

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