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Question
If \[\overrightarrow{a} = x \hat{i} + 2 \hat{j} - z \hat{k}\text{ and }\overrightarrow{b} = 3 \hat{i} - y \hat{j} + \hat{k}\] are two equal vectors, then write the value of x + y + z.
Solution
Given: \[\overrightarrow{a} = x \hat{i} + 2 \hat{j} - z \hat{k}\text{ and }\overrightarrow{b} = 3 \hat{i} - y \hat{j} + \hat{k}\]
Since the two vectors are equal. We have,
\[x \hat{i} + 2 \hat{j} - z \hat{k} = 3 \hat{i} - y \hat{j} + \hat{k} \]
\[ \Rightarrow x = 3, y = - 2, z = - 1\]
∴ \[x + y + z = 3 - 2 - 1 = 0\]
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