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Vector Algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVector Algebra2 Marks
Question
For given vectors, $\vec a = 2\hat i - \hat j + 2\hat k$ and $\vec b = - \hat i + \hat j - \hat k$, find the unit vector in the direction of the vector $\vec a + \vec b$.
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Answer

Given: Vectors $\vec a = 2\hat i - \hat j + 2\hat k$ and $\vec b = - \hat i + \hat j - \hat k$
$\therefore \vec a + \vec b = 2\hat i - \hat j + 2\hat k - \hat i + \hat j - \hat k $ $= \hat i + 0\hat j + \hat k$
Therefore, unit vector in the direction of $ {(\vec a + \vec b)} = \frac{{\hat i + 0\hat j + \hat k}}{{\sqrt {{{\left( 1 \right)}^2} + {{\left( 0 \right)}^2} + {{\left( 1 \right)}^2}} }}$
$= \frac{{\hat i + 0\hat j + \hat k}}{{\sqrt {1 + 0 + 1} }} = \frac{{\hat i + \hat k}}{{\sqrt 2 }} + \frac{1}{{\sqrt 2 }}\hat i + \frac{1}{{\sqrt 2 }}\hat k$

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