JEE Main & Advanced Physics Vectors Question Bank Fundamentals of Vectors

  • question_answer If \[\overrightarrow{A}=2\hat{i}+4\hat{j}-5\hat{k}\] the direction of cosines of the vector \[\overrightarrow{A}\] are

    A)            \[\frac{2}{\sqrt{45}},\frac{4}{\sqrt{45}}\,\text{and}\,\frac{-\,\text{5}}{\sqrt{\text{45}}}\]

    B)                                      \[\frac{1}{\sqrt{45}},\frac{2}{\sqrt{45}}\,\text{and}\,\frac{\text{3}}{\sqrt{\text{45}}}\]

    C)            \[\frac{4}{\sqrt{45}},\,0\,\text{and}\,\frac{\text{4}}{\sqrt{45}}\]  

    D)            \[\frac{3}{\sqrt{45}},\frac{2}{\sqrt{45}}\,\text{and}\,\frac{\text{5}}{\sqrt{\text{45}}}\]

    Correct Answer: A

    Solution :

                 \[\vec{A}=2\hat{i}+4\hat{j}-5\hat{k}\]\ \[|\overrightarrow{A}|\,=\sqrt{{{(2)}^{2}}+{{(4)}^{2}}+{{(-5)}^{2}}}\,=\,\sqrt{45}\]            \ \[\cos \alpha =\frac{2}{\sqrt{45}},\,\,\,\,\,\cos \beta =\frac{4}{\sqrt{45}},\,\,\,\,\cos \gamma =\frac{-5}{\sqrt{45}}\]


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