Vectors: Given that a = 2i + j and b = i + 3j, find....

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Given that a=2i+j and b=i+3j. find a) λ if a+λb is parallel to vector i. b) µ if µa+b is parallel to the vector j
 
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Given that a=2i+j and b=i+3j. find a) λ if a+λb is parallel to vector i. b) µ if µa+b is parallel to the vector j
\(\displaystyle \Large\bf{a}+\lambda\bf{b}\\\Large(2\bf{i}+\bf{j})+ \lambda (\bf{i}+3\bf{j})\\\Large(2+\lambda) \bf{i}+(1+3\lambda) \bf{j}\)

In order for the vector \(\displaystyle \Large\bf{\kappa i+\mu j}\) to be parallel to \(\displaystyle \Large\bf{i}\)
it is necessary that \(\displaystyle \Large \kappa\ne 0~\&~\mu=0\).
 
Given that a=2i+j and b=i+3j. find a) λ if a+λb is parallel to vector i. b) µ if µa+b is parallel to the vector j
If x is parallel to y then x cross y is zero. Use the distribution of cross products such as x cross y+z, scalar operations, i.e. (r x) cross y, and the cross product of the base vectors, for example i cross i.
 
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