જો mathop {rm{A}}limits^ to ,, = ,,4hat{i},, + ,,nhat{j},,

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3-1.Vectors

easy

જો $\mathop {\rm{A}}\limits^ \to \,\, = \,\,4\hat i\,\, + \,\,n\hat j\,\, - \,\,2\hat k$ અને $ \mathop B\limits^ \to \,\, = \,\,2\hat i\,\, + \;\,3\hat j\,\, + \;\,\hat k$ હોય તો $n$ કિમત ..... હોય જેથી $\mathop {\rm{A}}\limits^ \to \,\, \bot \,\,\mathop B\limits^ \to \,$ થાય .

$-2$

$-3$

$-4$

$-5$

Solution

બે પરસ્પર લંબ સદીશોનો ડોટ ગુણાકાર શૂન્ય હોય છે .

$\begin{array}{l}
\mathop A\limits^ \to .\,\,\mathop B\limits^ \to \, = \,\,0 \\
\,\therefore \,\,\left( {4\hat i\, + \,\,n\hat j\,\, – \,\,2\hat k} \right).\,\,\left( {2\hat i\,\, + \;\,3\hat j\,\, + \;\,\hat k} \right) = \,\,0\,\, \\ \Rightarrow \,\,\left( {4\,\, \times \,\,2} \right)\,\, + \,\,\left( {n\,\, \times \,\,3} \right)\,\, + \;\,\left( { – 2\,\, \times \,\,1} \right)\,\, = \,\,0\,\,\\ \Rightarrow \,\,3n\,\, = – 6\,\,\\ \Rightarrow \,\,n\,\, = \,\, – 2
\end{array}$

Standard 11

Physics