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The line (x+1)/(-10)=(y+3)/(-1)=(z-4)/1 ...

The line `(x+1)/(-10)=(y+3)/(-1)=(z-4)/1 and (x+10)/(-1)=(y+1)/(-3) =(z-1)/(4)` interest at the point.

A

(11,-4,5)

B

(-11,-4,5)

C

(11,4,-5)

D

(-11,-4,-5)

Text Solution

Verified by Experts

The correct Answer is:
B
Let `(x+1)/(-10)=(y+3)/(-1)=(z-4)/(1)=lambda_(1)`
`and (x+10)/(-1)=(y+1)/(-3)=(z-1)/(4)=lambda_(2)`
`"Then", (-10lambda_(1)-1-lambda_(2)-3,lambda_(1)+4)`
and `(-lambda_(2)-10,-3lambda_1-1, 4lambda_(2)+1)` are identical.
`-10lambda_(1)-1=-lambda_(2)-10,-lambda,-3=-3lambda_2-1`
and `lambda_(1)+4=4lambda_(2)+1`
`Rightarrow -10lambda_(1)+lambda_(2)=-9-lambda_(1)+3lambda_(2)=2`
`lambda_(1)-4lamda2=-3`
On solving, we get `lambda_(1)=lambda_(2)=1`
Intersection points is `(-10xx1-1, -1-3,1+4)i.e, (-11,-4,5)`
On solving, we get `x=-11, y=-4 and z=5`.
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