If $\overrightarrow A = 2\hat i + 4\hat j - 5\hat k$ the direction of cosines of the vector $\overrightarrow A $ are
If $\overrightarrow A = 2\hat i + 4\hat j - 5\hat k$ the direction of cosines of the vector $\overrightarrow A $ are
- A
$\frac{2}{{\sqrt {45} }},\frac{4}{{\sqrt {45} }}\,{\rm{and}}\,\frac{{ - \,{\rm{5}}}}{{\sqrt {{\rm{45}}} }}$
- B
$\frac{1}{{\sqrt {45} }},\frac{2}{{\sqrt {45} }}\,{\rm{and}}\,\frac{{\rm{3}}}{{\sqrt {{\rm{45}}} }}$
- C
$\frac{4}{{\sqrt {45} }},\,0\,{\rm{and}}\,\frac{{\rm{4}}}{{\sqrt {45} }}$
- D
$\frac{3}{{\sqrt {45} }},\frac{2}{{\sqrt {45} }}\,{\rm{and}}\,\frac{{\rm{5}}}{{\sqrt {{\rm{45}}} }}$
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- [AIPMT 1997]
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
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