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The point of intersection of the lines `(x-5)/3=(y-7)/(-1)=(z+2)/1a n d=(x+3)/(-36)=(y-3)/2=(z-6)/4` is a. `(21 ,5/3,(10)/3)` b. `(2,10 ,4)` c. `(-3,3,6)` d. `(5,7,-2)`

A

`(21,(5)/(3),(10)/(3))`

B

(2,10,4)

C

(-3,3,6)

D

(5,7,-2)

Text Solution

Verified by Experts

The correct Answer is:
a
Given lines are
`(x-5)/(3)=(y-7)/(-1)=(z+2)/(1)=r_(1)" "("say")`
and `(x+3)/(-36)=(y-3)/(2)=(z-6)/(4)=r_(2)" "("say")`
`becausex=3r_(1)+5=-36r_(2)-3,y=-r_(1)+7=3+2r_(2)`
and `z=r_(1)-2=4r_(2)+6`
On solving, we get
`x=12,y=(5)/(3),z=(10)/(3)`
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The point of intersection of the lines (x-5)/3=(y-7)/(-1)=(z+2)/1 and (x+3)/(-36)=(y-3)/2=(z-6)/4 is (A) (21, 5/3, 10/3) (B) (2,10,4) (C) (-3,3,6) (D) (5,7,-2)

The point of intersection of the lines (x-5)/(3)=(y-7)/(-1)=(z+2)/(1) and (x+3)/(-36)=(y-3)/(2)=(z-6)/(4) is (A) (21,(5)/(3),(10)/(3))(B)(2,10,4)(C)(-3,3,6)(D)(5,7,-2)

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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
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  3. The point of intersection of the lines (x-5)/3=(y-7)/(-1)=(z+2)/1a ...

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  5. Find the equation of a plane which passes through the point (3, 2, 0...

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  11. The plane vecr cdot vecn = q will cotain the line vecr = veca + lambda...

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  12. The projection of point P(vecp) on the plane vecr.vecn=q is (vecs), th...

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  13. The angle between hati and line of the intersection of the plane vecr...

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  14. The line (x+6)/5=(y+10)/3=(z+14)/8 is the hypotenuse of an isosceles ...

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  15. The equation of the plane which passes through the line of intersec...

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  16. Consider triangle A O B in the x-y plane, where A-=(1,0,0),B-=(0,2,0)a...

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  17. Let veca=hati+hatj and vecb=2hati-hatk. Then the point of intersection...

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  18. The co-ordinates of the point P on the line vecr =(hati +hatj + hatk...

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