Question

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

Answer 1

Given: $\overrightarrow{a}=x\hat{i}+2\hat{j}-z\hat{k}$ and $\overrightarrow{b}=3\hat{i}-y\hat{j}+\hat{k}$
Since the two vectors are equal. We have,
$$\begin{gathered} x\hat{i}+2\hat{j}-z\hat{k}=3\hat{i}-y\hat{j}+\hat{k} \\ \Rightarrow x=3,y=-2,z=-1 \end{gathered}$$
∴ $x+y+z=3-2-1=0$