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Vectors

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18 Mar 2008 20:58:27 IST

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friends ...........its urgent

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Express 2 icap - j cap + 3 k cap as the sum of a vector parallel and perpendicular to 2 i cap + 4 j cap - 2 k cap .

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sandeep ramesh

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18 Mar 2008 21:01:32 IST

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first find the angle between the vectors :)

arpan1

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18 Mar 2008 21:07:25 IST

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use the projection formula

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Vincent Khalwani

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18 Mar 2008 21:09:45 IST

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please explain me in detail with solution .

arpan1

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18 Mar 2008 21:13:16 IST

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thanks

here is the solution

u know the projection formula

projection of 2i - j +3k on 2i +4j - 2k is -1/4 (b vector)
this is for the parallel component

for perpendicular component
apply (a X b)/ mag (b) times b vector

Vincent Khalwani

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18 Mar 2008 21:15:54 IST

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you got it

arpan1

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18 Mar 2008 21:24:22 IST

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got the solution vincent, right

Vincent Khalwani

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18 Mar 2008 21:26:34 IST

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give me the solution damned

arpan1

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18 Mar 2008 21:28:12 IST

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i have already given the solution . move ur cursor upwards towards my post to find it...

Vincent Khalwani

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18 Mar 2008 21:32:29 IST

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I didn't understand that parallel part friend..

arpan1

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18 Mar 2008 21:35:10 IST

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see for parallel part u have

(a.b)/mag(b) times b vector

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ram kumar

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18 Mar 2008 21:48:12 IST

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let a = 2i-j+3k

b = 2i+4j-2k

now let c be parallel to b and d be perpendicular to b

we have to express a = c + d

since c is parallel to b . let c = mb = 2m i + 4m j - 2m k

d=a-c

d= 2i - j +3k - 2m i - 4m j +2m k

d= (2-2m)i - (1+4m)j + (3+2m)k

since d is perpendicular to b ....... their dot product is 0

(2-2m)2 -(1+4m)4 -2(3+2m) =0

4 - 4m -4 -16m -6 -4m = 0

-24m = 6

m = -(1/4)

so c = - i/2 - j + k/2

d = 2i - j +3k +i/2 + j -k/2

d = (5/2)i + (5/2)k

thus a = c + d

where c is parallel to b and d is perpendicular to b

clear with my sloution.........????

Vincent Khalwani

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18 Mar 2008 21:54:25 IST

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absolutely .......thank you very much

arpan1

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18 Mar 2008 22:02:07 IST

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i hope my solution is ok for getting full marks in cbse

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