Column I | Column II |
(a) \[\vec{A}.\,\vec{B}=0\] | (i) \[\theta =0\] |
(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) \[\theta =\,{{60}^{o}}\] |
Answer:
(a) \[\vec{A}.\vec{B}\,=AB\,\cos
\,\theta \,=0\] if \[\theta =\,{{90}^{o}}\]
\[\therefore \] \[\,(a)\,\to
\,(ii)\]
(b) \[\vec{A}.\vec{B}\,=\,AB\,\,\cos
\theta =\,8\] if
\[\cos \,\,\theta =\,1\] or
\[\theta \,=\,{{0}^{o}}\]
\[\therefore \,(b)\,\,\to
\,\,(i)\]
(c) \[\vec{A}\,.\vec{B}\,=\,AB\,\,\cos
\theta \,=\,4\] if
\[\cos \theta \,=\,\frac{1}{2}\]or \[\theta \,=\,{{60}^{o}}\]
\[\therefore \,\,(c)\,\,\to
\,(iv)\]
(d) \[\vec{A}\,.\vec{B}\,\,=\,AB\,\,\cos
\,\theta \,=-8\] of
\[\cos \theta =\,-1\] or
\[\theta \,=\,{{180}^{0}}\]
\[\therefore \,(d)\,\to
\,(iii)\]
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