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यदि `veca = a_(1)hati + a_(2)hatj` तथा `vecb =b_(1)hati +b_(2)hatj` शूनयेत्तर सदिश हैं तो साबित करें कि ये समान्तर होंगे यदि और केवल यदि `a_(1)b_(2) -a_(2)b_(1)=0`. |
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Answer» `veca || vecb ltimplies veca = lambda vecb`, जहाँ `lambda ne 0` `ltimplies a_(1)hati + a_(2)hatj = lambda(b_(1)hati + b_(2)hatj) ltimplies a_(1)hati + a_(2)hatj = lambda b_(1)hati + lambdab_(2)hatj` `ltimplies a_(1) = lambda b_(1)` तथा `a_(2) = lambdab_(2)` `ltimplies a_(1)/a_(2) =b_(1)/b_(2) ltimplies a_(1)b_(2) -a_(2)b_(1)=0` अतः दिए हुए सदिश `veca` और `vecb` समान्तर होंगे यदि और केवल यदि `a_(1)b_(2) - a_(2)b_(1)=0`. |
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