Q131 / 160 · WBJEE 2011 · Physics

Given \(\overrightarrow{\mathrm{A}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}\) and \(\overrightarrow{\mathrm{B}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}\). The component of vector \(\overrightarrow{\mathrm{A}}\) along vector \(\overrightarrow{\mathrm{B}}\) is

  • A
    \(\frac{1}{\sqrt{2}}\)
  • B
    \(\frac{3}{\sqrt{2}}\)
  • Correct answer
    C
    \(\frac{5}{\sqrt{2}}\)
  • D
    \(\frac{7}{\sqrt{2}}\)

Solution

Hints: Component of \(\vec{A}\) along \(\vec{B}=\vec{A} \cdot \frac{\vec{B}}{|\vec{B}|}\) Component of \(\overrightarrow{\mathrm{A}}\) along \(\overrightarrow{\mathrm{B}}=\frac{5}{\sqrt{2}}\)

Hence, the correct answer is option: 'C'.

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