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The equation of a line which passe...

The equation of a line which passes through the point ` ( 1, 2 , 3 ) ` and is parallel to the vector ` 3 hati + 2 hatj - 2 hatk ` , is

A

` r = ( 3 hati + 2hatj - 2 hatk ) + lamda ( hati + 2 hatj + 3 hatk ) `

B

` r = ( hati + 2 hatj + 3 hatk ) + lamda ( 3 hati + 2 hatj - 2 hatk ) `

C

` r = ( hati + 2 hatj + 3hatk ) + lamda ( 2 hati - 5hatk ) `

D

` r = ( hati + 2hatj + 3 hatk ) + lamda ( 4 hati + 4 hatj + hatk ) `

Text Solution

Verified by Experts

The correct Answer is:
B
It is given that the line passes through the point ` A ( 1, 2, 3 ) `
The position vector of A is a = ` hati + 2 hatj + 3hatk `
and parallel to a vector ` b = 3hati + 2hatj - 2 hatk `
The required equation of the line is
` r = hati + 2 hatj + 3 hatk + lamda ( 3hati + 2 hatj - 2 hatk ) `
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-LINE-Exercise 2(Miscellaneous Problems)
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  2. The length of the perpendicular from P(1,6,3) to the line x/1=(y-1)/(2...

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  3. The equation of a line which passes through the point ( 1, 2...

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  4. P is a point on the line segment joining the points (3, 2, ...

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

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  6. Find the vector and the cartesian equations of the lines that passes ...

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

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  8. 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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  9. 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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  10. Find the equation of the perpendicular from point (3,-1,11) to line x...

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

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

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  14. Match the following columns.

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

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

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

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

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

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