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Value of lamda such that the line (x-1)/...

Value of `lamda` such that the line `(x-1)/(2)=(y-1)/(3)=(z-1)/(lamda)` is `bot` to normal to the plane `vecr.(2veci+3vecj+4veck)=0` is

A

`-(13)/(4)`

B

`-(17)/(4)`

C

4

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
Since line is parallel to the plane, vector `2hati+3hatj+lamdahatk` is perpendicular to the normal to the plane
`2hati + 3hatj+ 4hatk`
`rArr" "2xx2+ 3xx3 + 4lamda =0`
or `" "lamda = - (13)/(4)`
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
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  3. Equation of the pane passing through the points (2,2,1)a n d(9,3,6),...

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  7. The vector equation of the plane passing through the origin and the li...

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  8. The two lines vecr=veca+veclamda(vecbxxvecc) and vecr=vecb+mu(veccxxve...

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  9. The projection of the line (x+1)/(-1)=y/2=(z-1)/3 on the plane x-2y+z=...

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  10. The direction cosines of a line satisfy the relations lambda(l+m)=n ...

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  12. Find the angle between the lines whose direction cosines are given by ...

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  15. What is the nature of the intersection of the set of planes x+a y+(...

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  16. Find the equation of a straight line in the plane vecr.vecn=d which is...

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  17. What is the equation of the plane which passes through the z-axis and ...

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  18. A straight line L on the xy-plane bisects the angle between O Xa n dO ...

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  19. For what value (s) of a will the two points (1,a ,1)a n d(-3,0,a) l...

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