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Consider the line L 1 : x +1/3 = y+ 2/...

Consider the line L 1 : x +1/3 = y+ 2/1= z +1/2 L2 : x-2/1= y+2/2= z-3/3 The unit vector perpendicular to both L 1 and L 2 lines is

A

`(-hati+7hatj+7hatk)/(sqrt(99))`

B

`(-hati-7hatj+5hatk)/(5sqrt(3))`

C

`(-hati+7hatj+5hatk)/(5sqrt(3))`

D

`(7hati-7hatj-hatk)/(sqrt(99))`

Text Solution

Verified by Experts

The correct Answer is:
b
`|{:(hati,,hatj,,hatk),(3,,1,,2), (1,,2,,3):}|=-hati-7hatj+5hatk`
Hence, the unit vector will be `(-hati-7hatj+5hatk)/(5sqrt3)`
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Knowledge Check

  • Perpendiculars are drawn from points on the line (x + 2)/(2) = (y +1)/(-1) = (z)/(3) to the plane x + y + z = 3 . The feet of perpendiculars lie on the line

    A
    `(x)/(5) = (y -1)/(8) = (z -2)/(-13)`
    B
    `(x)/(2) = (y -1)/(3) = (z -2)/(-5)`
    C
    `(x)/(4) = (y-1)/(3) = (z-2)/(-7)`
    D
    `(x)/(2) = (y-1)/(-7) = (z-2)/(5)`

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