Question

For given vectors, a=2i-j+2k and b =-i+j-k find the unit vector in the direction of the vector a+b

Answer 1

The unit vector in the direction of the vector $\vec{c}$ is $\frac{\vec{c}}{|\vec{c}|}$.

The given vectors are $\vec{a}=2\bold{i}-\bold{j}+2\bold{k} , \vec{b} =-\bold{i}+\bold{j}-\bold{k}$.

Now,

$\vec{a}+ \vec{b} =2\bold{i}-\bold{j}+2\bold{k} -\bold{i}+\bold{j}-\bold{k}\\ \vec{a}+ \vec{b} =\bold{i}+\bold{k}$.

The unit vector in the direction of $\vec{a}+ \vec{b}$ is

$\frac{ \bold{i}+\bold{k}}{|\bold{i}+\bold{k}|} =\frac{ \bold{i}+\bold{k}}{\sqrt{1^2+1^2}} =\frac{1}{\sqrt{2}}\bold{i}+\frac{1}{\sqrt{2}}\bold{k}$

Answer 2

Step-by-step explanation:

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