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

[xxixiii]

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​

 

[pka]

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 $\displaystyle \Large \kappa\ne 0~\&~\mu=0$.

 

[Ishuda]

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.