Categories > vectors > fundamental-of-vectors > With respect to a rectangular cartesian coordinate system, three vectors are expressed as $\vec a = 4\hat i - \hat j$, $\vec b = - 3\hat i + 2\hat j$ and $\vec c = - \hat k$ where $\hat i,\,\hat j,\,\hat k$ are unit vectors, along the X, Y and Z-axis respectively. The unit vectors $\hat r$along the direction of sum of these vector is

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Question: With respect to a rectangular cartesian coordinate system, three vectors are expressed as $\vec a = 4\hat i - \hat j$, $\vec b = - 3\hat i + 2\hat j$ and $\vec c = - \hat k$ where $\hat i,\,\hat j,\,\hat k$ are unit vectors, along the X, Y and Z-axis respectively. The unit vectors $\hat r$along the direction of sum of these vector is


1) $\hat r = \frac{1}{{\sqrt 3 }}(\hat i + \hat j - \hat k)$
2) $\hat r = \frac{1}{{\sqrt 2 }}(\hat i + \hat j - \hat k)$
3) $\hat r = \frac{1}{3}(\hat i - \hat j + \hat k)$
4) $\hat r = \frac{1}{{\sqrt 2 }}(\hat i + \hat j + \hat k)$
Solution: Explanation: Explanation
fundamental-of-vectors

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