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Question

$$ \text{If} \,\, \vec { a } =5\hat { i } +4\hat { j } -6\hat { k } ,\vec{ b } =-2\hat { i } ,+2\hat { j } +3\hat { k } \,\,and\,\, \vec{ c } =4\hat { i } +3\hat { j } +2\hat { k } $$ then

A
$$ \vec{ r } =\vec{ a } -\vec{ b } +\vec{ c } =11\hat { i } +5\hat { j } -7\hat { k } $$
B
$$ \vec{ r } =\vec{ a } -\vec{ b } +\vec{ c } =9\hat { i } +4\hat { j } -6\hat { k } $$
C
The angle between $$ \vec{ r }$$ and the z-axis is
$$cos^{-1} \left( \dfrac { -7 }{ \sqrt { 195 } } \right) $$
D
The angle between $$ \vec{ r }$$ and the z-axis is $$cos^{-1} \left( \dfrac { -6 }{ \sqrt { 186 } } \right) $$
Solution
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Correct option is C. The angle between $$ \vec{ r }$$ and the z-axis is
$$cos^{-1} \left( \dfrac { -7 }{ \sqrt { 195 } } \right) $$

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