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The lines vecr=(2hati-3hatj+7hatk)+lam...

The lines
`vecr=(2hati-3hatj+7hatk)+lamda(2hati+phatj+5hatk)`
and `vecr=(hati+2hatj+3hatk)+mu(3hati+phatj+phatk)` are perpendicular it `p=`

A

`1,-6`

B

`1,6`

C

`-1,-6`

D

`-1,6`

Text Solution

Verified by Experts

The correct Answer is:
D
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The equation of line passing through (3,-1,2) and perpendicular to the lines vecr=(hati+hatj-hatk)+lamda(2hati-2hatj+hatk) and vecr=(2hati+hatj-3hatk) +mu(hati-2hatj+2hatk) is

If d is the shortest distance between the lines vecr =(3hati +5hatj + 7hatk)+lambda (hati +2hatj +hatk) and vecr = (-hati -hatj-hatk)+mu(7hati-6hatj+hatk) then 125d^(2) is equal to ____________.

Find the vector and Cartesian equations of a plane containing the two lines vecr=(2hati+hatj-3hatk)+lambda(hati+2hatj+5hatk) and vecr=(3hati+3hatj+2hatk)+mu(3hati-2hatj+5hatk) .

The angle between the lines vecr=(2hati-5hatj+hatk)+lamda(3hati+2hatj+6hatk)andvecr=(7hati-6hatk)+mu(hati+2hatj+2hatk) is

Show that the lines vecr=(2hatj-3hatk)+lambda(hati+2hatj+3hatk) and vecr = (2hati+6hatj+3hatk)+mu(2hati+3hatj+4hatk) are coplanar. Also the find the equation of the plane passing through these lines.

Find the shortest distance between the lines vecr = 2hati - hatj + hatk + lambda(3hati - 2hatj + 5hatk), vecr = 3hati + 2hatj - 4hatk + mu(4hati - hatj + 3hatk)

TARGET PUBLICATION-LINE-Critical Thinking
  1. D.c.s of a line segment AB are (-2)/(sqrt(17)),(3)/(sqrt(17)),(-2)/(sq...

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  2. The lines barr=(2hati+hatj-3hatk)+((t)/(sqrt(6)))(2hati-hatj+hatk)an...

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  3. The lines vecr=(2hati-3hatj+7hatk)+lamda(2hati+phatj+5hatk) and ve...

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  4. If the lines (x-1)/(2)=(y-1)/(lambda)=(z-3)/(0) and (x-2)/(1)=(y-3)/...

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  5. The lines and (x-1)/(3)=(y-2)/(4)=(z-3)/(5) (x-1)/(2)=(y-2)/(3)=(z-3)...

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

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  7. If the sum of the squares of the distances of a point from the three c...

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  8. The foot of perpendicular from the point (1,2,3) to the line (x)/(2)=(...

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  9. The co-ordinates of the foot of the perpendicular from the point (3,-1...

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  10. Find the foot of the perpendicular from the point (0,2,3) on the line ...

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  11. The length of perpendicular from the origin to the line vecr=(4hati=2h...

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  12. The length of the perpendicular drawn from the point (5,4,-1) on the l...

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  13. The length of perpendicular from (2, -1, 5) to the line (x-11)/(10)=(y...

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  14. The co-ordinates of a point on the line (x-1)/(2)=(y+1)/(-3)=z at a di...

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  15. A line passes through two points A(2,-3,-1) and B(8,-1,2). The coordin...

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  16. Find the equation of the perpendicular drawn from the point (2,4,-1) t...

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  17. Two lines (x)/(1)=(y)/(2)=(z)/(3)and(x+1)/(1)=(y+2)/(2)=(z+3)/(3) are

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  18. Find the shortest distance between the following pair of line: vecr=(1...

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  19. The shortest distance between lines barr=(lambda-1)hati+(lambda+1)hatj...

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  20. If the lines (x-1)/(k)=(y+1)/(3)=(z-1)/(4)and(x-3)/(1)=(2y-9)/(2k)=(z)...

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