Vector P =6 hat{ i }+4 √{2} hat{ j }+4 √{2} hat{ k } makes angle from z -axis equal to

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3-1.Vectors

normal

Vector $P =6 \hat{ i }+4 \sqrt{2} \hat{ j }+4 \sqrt{2} \hat{ k }$ makes angle from $z$-axis equal to

A$\cos ^{-1}\left(\frac{\sqrt{2}}{5}\right)$

B$\cos ^{-1}(2 \sqrt{2})$

C$\cos ^{-1}\left(\frac{2 \sqrt{2}}{5}\right)$

DNone of these

Solution

(c)
$\gamma=\cos ^{-1}\left(\frac{P_z}{P}\right)$
Here, $\quad P_z=4 \sqrt{2}$
$\text { and } \quad P=\sqrt{(6)^2+\left(4 \sqrt{2)^2}+\left(4 \sqrt{2)^2}\right.\right.}=10$

Standard 11

Physics

If $\left| {\vec A } \right|\, = \,2$ and $\left| {\vec B } \right|\, = \,4$ then match the relation in Column $-I$ with the angle $\theta $ between $\vec A$ and $\vec B$ in Column $-II$.

Column $-I$ Column $-II$

$(a)$ $\vec A \,.\,\,\vec B \, = \,\,0$ $(i)$ $\theta = \,{0^o}$

$(b)$ $\vec A \,.\,\,\vec B \, = \,\,+8$ $(ii)$ $\theta = \,{90^o}$

$(c)$ $\vec A \,.\,\,\vec B \, = \,\,4$ $(iii)$ $\theta = \,{180^o}$

$(d)$ $\vec A \,.\,\,\vec B \, = \,\,-8$ $(iv)$ $\theta = \,{60^o}$

medium

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