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  • If three vectors are a(1 ,1,1) ,b (4,-2,3), c(1,-2,1) then find the vector of magnitude 6 unit which is parallel to the vector 2a-b+3c.

If three vectors are a(1 ,1,1) ,b (4,-2,3), c(1,-2,1) then find the vector of magnitude 6 unit which is parallel to the vector 2a-b+3c.

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eginarrayl extGiven that,\ veca=left(1,1,1 ight), vecb=left(4,-2,3 ight) & vecc=left(1,-2,1 ight)\ vecr=2veca-vecb+3vecc \ vecr=2left(i+j+k ight)-left(4i-2j+3k ight)+3left(i-2j+k ight)=i+2k\ extUnit vector is left(vecr ight)=fraci+2ksqrt5\ extLet vecA, extis parallel to vecr extand magnitude is 6.\ vecA=6left(fraci+2ksqrt5 ight)endarray

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Deependra Verma

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