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Consider the lines L 1 : ( x - 1 ...

Consider the lines ` L _ 1 : ( x - 1 )/ ( 3 ) = ( y + 2 ) / ( 1 ) = ( z + 1 ) / ( 2 ) `
` L _ 2 : ( x - 2) / ( 1 ) = ( y + 2 ) / ( 2 ) = ( z - 3 )/ ( 3 ) ` The unit vector perpendicular to both ` L _ 1 and L_ 2 ` is

A

` ( 1 ) / ( sqrt (99)) ( - hati + 7 hatj +7hatk ) `

B

` ( 1 ) / ( 5 sqrt3) ( - hati - 7 hatj + 5 hatk ) `

C

` ( 1 ) / ( 5sqrt 3 ) ( - hati+ 7 hatj + 5 hatk ) `

D

` ( 1 ) /( sqrt ( 99)) ( 7 hati - 7hatj - hatk ) `

Text Solution

Verified by Experts

The correct Answer is:
B
Lines `L _ 1 and L _ 2 ` are parallel to the vectors
` b _ 1 = 3 hati + hatj + 2 hatk and b _ 2 = hati + 3 hatj + 3 hatk ` respectively.
Therefore, a unit vector perpendicular to both `L _ 1 and L _ 2 ` is
` hatn = ( b _ 1 xx b _ 2 ) / ( | b _ 1 xx b _ 2 | ) `
` b _ 1 xx b _ 2 = |{:( hati , hatj , hatk ) , ( 3, 1, 2 ) , (1, 2, 3 ) :}| = - hati - 7 hatj + 5hatk `
` therefore hatn = ( 1 ) / ( 5sqrt 3 ) ( - hati - 7 hatj + 5 hatk ) `
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-LINE-Exercise 2(Miscellaneous Problems)
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  3. P is a point on the line segment joining the points (3, 2, ...

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  4. The equaton of the line in vector and cartesian from that pas...

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  6. The equation of a line 4x-4y-z+11=0=x+2y-z-1 can be put as

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  7. The line (x-2)/3=(y+1)/2=(z-1)/1 intersects the curve x y=c^(I2),z=0 i...

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

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  9. Find the equation of the perpendicular from point (3,-1,11) to line x...

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  10. The line passing through the points (5,1,a) and (3,b,1) crosses the y...

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

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  12. Consider the line L 1 : (x+1)/3=( y-2)/1= (z+1)/2, L 2 : (x-2)/1=(...

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  13. Match the following columns.

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  14. Find the equation of a line passing through (1,-1,0) and parallel to t...

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  15. The direction cosines of the line x-y+2z=5, 3x+y+z=6 are

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  16. The length of the perpendicular drawn from (1,2,3) to the line (x-6)...

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  17. The straight line (x-3)/3=(y-2)/1=(z-1)/0 is Parallel to x-axis Parall...

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

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  19. If the lines x = 1 + s, y = - 3 - lamda s , z = 1 + la...

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  20. Consider the lines L 1 : ( x - 1 )/ ( 3 ) = ( y + 2 ) / ...

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