Question

If $\overrightarrow{a}=x\hat{i}+2\hat{j}-z\hat{k}$ and $\overrightarrow{b}=3\hat{i}-y\hat{j}+\hat{k}$ are two equal vectors, then write the value of $x+y+z$.

Answer 1

Equate the vectors $\overrightarrow{a}=x\hat{i}+2\hat{j}-z\hat{k}$ and $\overrightarrow{b}=3\hat{i}-y\hat{j}+\hat{k}$ by writing them in the component form that is

$\overrightarrow{a}=⟨x,2,-z⟩$ and $\overrightarrow{b}=⟨3,-y,1⟩$

Then the equate the vectors as follows:

$⟨x,2,-z⟩=⟨3,-y,1⟩$

implies $x=3,y=-2,z=-1$

Therefore, $x+y+z=3-2-1=0$

Hence, $x+y+z=0$.