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

Consider the line ` L 1 : (x +1)/3 = (y +2)/1 = (z+ 1)/2, L2 : (x-2)/1 = (y+2)/2 = (z-3)/3 `

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
The equations of given lines in vector form may be written as `L_(1):vecr=(-hati-2hatj-hatk)+lambda(3hati+hatj+2hatk)`
and `" "L_(2):vecr=(2hati-2hatj+3hatk)+mu(hati+2hatj+3hatk)`
Since, the vector is perpendicular to both `L_(1)` and `L_(2).`
`|{:(hati,hatj, hatk),(3,1,2),(1,2,3):}|=-hati-7hatj+5hatk`
`:.` Required unit vector
`=((-hati-7hatj+5hatk))/(sqrt((-1)^(2)+(-7)^(2)+(5)^(2)))=(1)/(5sqrt(3))(-hati-7hatj+5hatk)`
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