JEE Main & Advanced Mathematics Vector Algebra Question Bank Modulus of vector Algebra of vectors

  • question_answer
    If the position vectors of A and B are \[\mathbf{i}+3\mathbf{j}-7\mathbf{k}\] and \[5\mathbf{i}-2\mathbf{j}+4\mathbf{k},\] then the direction cosine of \[\overrightarrow{AB}\] along y-axis is                                                                                                  [MNR 1989]

    A) \[\frac{4}{\sqrt{162}}\]       

    B) \[-\frac{5}{\sqrt{162}}\]

    C) 5             

    D) 11

    Correct Answer: B

    Solution :

    \[\overrightarrow{AB}=4\mathbf{i}-5\mathbf{j}+11\mathbf{k}\] Direction cosine along \[y-\]axis \[=\frac{-5}{\sqrt{16+25+121}}=\frac{-5}{\sqrt{162}}.\]


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