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If the lines (x-2)/1=(y-3)/1)(z-4)/(-k) ...

If the lines `(x-2)/1=(y-3)/1)(z-4)/(-k) and (x-1)/k=(y-4)/2=(z-5)/1` are coplanar then k can have

A

any value

B

exactly one value

C

exactly two values

D

exactly three values

Text Solution

Verified by Experts

The correct Answer is:
C
Condition of coplanar
`|{:(2-1,3-4,4-5),(1,1,-k),(k,2,1):}|=0rArr|{:(1,-1,-1),(1,1,-k),(k,2,1):}|=0`
`rArr" "1(1+2k)+(1+k^(2))-(2-k)=0`
`rArr" "k^(2)+2k+k=0`
`rArr" "k^(2)+3k=0rArrk=0,-3`
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  2. The distance of a plane Ax+By+Cz=D from the point (x(1),y(1),z(1)) is

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  3. If the distance of the point P(1,-2,1) from the plane x+2y-2z=alpha,...

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  4. If the foot of the perpendicular from O(0,0,0) to a plane is P(1,2,2)....

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  5. If (2,-1,3) is the foot of the perpendicular down from the origin to t...

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  6. let Q be the foot of perpendicular from the origin to the plane 4x-3y+...

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  7. The distance of the point (1,-5,9) from the plane x-y+z = 5 measured a...

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  8. If the straight lines x 1 y 1 z 2 k 2 and x 1 y 1 z 5 2 k are copl...

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  9. If the straighat lines x=1+s,y=-3-lamdas,z=1+lamdas and x=t/2,y=1+t,z=...

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  10. Show that the lines (x+1)/-3=(y-3)/2=(z+2)/1 and x/1=(y-7)/-3=(z+7)/2 ...

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  11. If the lines (x+1)/(2)=(y-1)/(1)=(z+1)/(3)and(x+2)/(2)=(y-k)/(3)=(z)/(...

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  12. Find the shortest distance between the lines (x-1)/2=(y-2)/3=(z-3)/...

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  13. Find the equation of a plane which passes through the point (3, 2, ...

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  14. If the lines (x-2)/1=(y-3)/1)(z-4)/(-k) and (x-1)/k=(y-4)/2=(z-5)/1 ar...

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  15. The coordinate of the foot of perpendicular drawn from origin to a pla...

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  16. Let a plane passes through the point P(-1,-1,1) and also passes throug...

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