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[" The scalar product of the vector "vec a=hat i+hat j+hat k" with a unit vector along "],[" the sum of the vectors "vec b=2hat i+4hat j-5hat k" and "vec c=lambdahat i+2hat j+3hat k" is "],[" equal to "1." Find the value of "lambda" and hence find the unit vector along "],[vec b+vec c" ."]

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The scalar product of the vector vec a= hat i+ hat j+ hat k with a unit vector along the sum of the vectors vec b=2 hat i+4 hat j-5 hat k\ a n d\ vec c=lambda hat i+2 hat j+3 hat k is equal to 1. Find the value of lambda and hence find the unit vector along vec b+ vec cdot

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