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Let A( vec a)a n dB( vec b) be points on...

Let `A( vec a)a n dB( vec b)` be points on two skew lines ` vec r= vec a+lambda vec pa n d vec r= vec b+u vec q` and the shortest distance between the skew lines is `1, w h e r e vec pa n d vec q` are unit vectors forming adjacent sides of a parallelogram enclosing an area of 1/2 units. If angle between`A B` and the line of shortest distance is `60^0,` then `A B=` a. `1/2` b. `2` c. `1` d. `lambda R={10}`

A

`(1)/(2)`

B

2

C

1

D

`lamdaepsiR-{0}`

Text Solution

Verified by Experts

The correct Answer is:
b
`1=|(vecb-veca).(vecpxxvecq)/(|vecpxxq|)|`
or `|vecb-veca|cos60^(@)=1impliesAB=2`
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
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  2. The equation of the plane which passes through the point of interse...

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  3. Let A( vec a)a n dB( vec b) be points on two skew lines vec r= vec a+...

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  4. Let A(1,1,1),B(23,5)a n dC(-1,0,2) be three points, then equation of a...

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  5. The point on the line (x-2)/1=(y+3)/(-2)=(z+5)/(-2) at a distance of 6...

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  6. The coordinates o the foot of the perpendicular drawn from the orig...

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  7. about to only mathematics

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  8. The length of projection of the line segment joining the points (1,...

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  9. The number of planes that are equidistant from four non-coplanar po...

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  10. In a three-dimensional coordinate system, P ,Q ,a n dR are images o...

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  11. A plane passing through (1,1,1) cuts positive direction of coordinates...

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  12. If lines x=y=za n dx=y/2=z/3 and third line passing through (1,1,1) fo...

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  13. Find the point of intersection of line passing through (0,0,1) and t...

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  14. Shortest distance between the lines (x-1)/1=(y-1)/1=(z-1)/1a n d(x-...

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  15. Distance of point P(vecP) from the plane vecr.vecn=0 is

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  16. The reflection of the point veca in the plane vecr.vecn=q is (A) veca+...

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  17. The angle theta between the line vecr=veca+lambdavecb and the plane ve...

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  18. If a line makes an angel of pi/4 with the positive direction of eac...

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  19. The ratio in which the plane vec rdot( vec i-2 vec j+3 vec k)=17 d...

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