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Vectors

Cool goIITian

Joined:	23 Jun 2011
Post:	65

29 May 2012 22:46:21 IST

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3D geometry

Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Vectors

Find the Cartesian eqution of line 6x-2=3y+1=2z-2. Find its direction ratios and also the vector eqution of the line.

Comments (4)

Aman Sharma

Cool goIITian

Joined: 29 May 2012

Posts: 37

29 May 2012 23:45:23 IST

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Cartesian equation is the one which you posted.

To find direction rations,make x,y and z independent of any terms

So, line is

6x-2=3y+1=2z-2

6(x- 1/3)= 3(y+1/3)= 2(z-1)

(x- 1/3)/(1/6)= (y + 1/3)/(1/3)= (z-1)/(1/2)

So direction ratios are 1/6,1/3 and 1/2

Since this line passes through (1/3,-1/3,1) and has above direction ratios

Its vector eqn is given by

[(1/3)i + (-1/3)j +k] + m[(1/6)i + (1/3)j + (1/2)k]=0

where m is any constant.

Benita

Cool goIITian

Joined: 23 Jun 2011

Posts: 65

30 May 2012 00:59:57 IST

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Thanks a lot:)

Benita

Cool goIITian

Joined: 23 Jun 2011

Posts: 65

30 May 2012 01:13:02 IST

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Could you tell me what exactly vector equation is?

Aman Sharma

Cool goIITian

Joined: 29 May 2012

Posts: 37

30 May 2012 09:18:53 IST

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If any line passes through a point having position vector a and direction cosines b,then its vector equation is given by a+m.b=0 where m is any constant.

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