(a) Find the unit vector which is p...
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(a) Find the unit vector which is parallel to the vector A = 2 i+3 j-k. () Find the unit vector which is perpendicular to both of the vectors A = 2i and B = 3 i+4j+12

JEE/Engineering Exams
Physics
Solution
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(i) ( bar{A}=2 hat{1}+3 hat{j} cdot-hat{k} ) [ |hat{A}|=sqrt{2^{2}+3^{2}+(-1)^{2}}=sqrt{4+9+1} ] ( =sqrt{14} ) ( begin{aligned} text { writ veitor parallel to } A & text { A } &=frac{A}{1 vec{A} backslash}=frac{2 hat{1}+3 hat{jmath}-hat{k}}{sqrt{14}} end{aligned} ) (ii) ( vec{A}=2 hat{1} ; vec{B}=3 hat{lambda}+4 hat{jmath}+12 hat{k} ) ( vec{A} times vec{B}=2 hat{imath} times(3 hat{imath}+4 hat{jmath}+12 hat{k}) ) ( =8 hat{k}-24 hat{jmath} ) ( |vec{A} times vec{B}|=sqrt{640}=8 sqrt{10} ) Vuit vator perpendicular to Á& is ( =frac{A^{prime} times vec{B}}{|vec{A} times vec{B}|}=frac{8 hat{k}-24 hat{jmath}}{8 sqrt{10}} ) ( =frac{-3 hat{j}+hat{k}}{sqrt{10}} )
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