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VECTOR ALGEBRA — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVECTOR ALGEBRA2 Marks
Question
If $\vec{\text{a}}=\text{x}\hat{\text{i}}+2\hat{\text{j}}-\text{z}\hat{\text{k}}$ and $\vec{\text{b}}=3\hat{\text{i}}-\text{y}\hat{\text{j}}+\hat{\text{k}}$ are two equal vectors, then write the value of x + y + z.
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Answer

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

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