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Vectors

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11 Apr 2011 20:03:34 IST

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let a=i+j+k and b=2i+3j+k find the vector component of b in the direction of a and perpendicular

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let a=i+j+k and b=2i+3j+kfind the vector component of b in the direction of a and perpendicular to a.

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ankurkumar

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Joined: 12 Jan 2010

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25 Apr 2011 11:01:10 IST

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consider b as ths sum of Aa+c where A is scalar and b is the vector perpendicular to the vector a .now rewrite it to get c=b-Aa take dot with a to get A as c.a=0 now u can find c.

edison

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30 Sep 2011 17:17:47 IST

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vector component of b in the direction of a= b cos(t)
vector component of b in the direction of perpendicular to a =b sint, where t= angle between a and b

Now, a.b = a b cos(t), where a = sqrt(1²+1²+1²) and b=sqrt(2²+3²+1²), a.b =1*2+1*3+1*1 = 6

so you will get the value of cos(t). Calculate sin t =sqrt(1-cos²t)

put the values of cos(t) and sin t above and get the result

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