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3-1.Vectors
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જો ${\rm{2\hat i}}\,\, + \,\,{\rm{3\hat j}}\,\, + \,\,{\rm{8\hat k}}$ સદિશ એ ${\rm{4\hat j}}\,\,{\rm{ - }}\,\,{\rm{4\hat i}}\,\, + \;\,\alpha {\rm{\hat k}}$ સદિશને લંબ હોય તો $\alpha $ ની કિંમત કેટલી હોય ?
A
$-1$
B
$0.5$
C
$-0.5$
D
$1$
Solution
$\begin{array}{l}
\left( {\,2\hat i\,\, + \;\;3\hat j\,\, + \;\,8\hat k} \right).\left( {4\hat j\,\, – \,\,4i\,\, + \;\,\alpha \hat k} \right)\,\, = \,\,0\\
\Rightarrow \,\, – 8\,\, + \;\;12\,\, + \;\,8\alpha \,\, = \,\,0\,\,\, \Rightarrow \,\,8\alpha \,\, = \,\, – 4\,\,\,\, \Rightarrow \,\,\alpha \,\, = \,\, – \frac{8}{4}\,\, = \,\, – \frac{1}{2}
\end{array}$
Standard 11
Physics
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