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Vectors — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsVectors2 Marks
MCQ
If $\bar{a}=2 \hat{i}+5 \hat{j}$ and $\bar{b}=2 \hat{i}-\hat{j}$, then the unit vector along $\bar{a}+\bar{b}$ will be
  • A
    $\frac{\hat{ i }-\hat{ j }}{\sqrt{2}}$
  • B
    $\hat{ i }+\hat{ j }$
  • C
    $\sqrt{2}(\hat{ i }+\hat{ j })$
  • ✓
    $\frac{\hat{ i }+\hat{ j }}{\sqrt{2}}$
✓

Answer

Correct option: D.
$\frac{\hat{ i }+\hat{ j }}{\sqrt{2}}$
(D) $\overline{ a }+\overline{ b }=4 \hat{ i }+4 \hat{ j }$
∴ Unit vector $=\frac{4(\hat{ i }+\hat{ j })}{\sqrt{32}}=\frac{\hat{ i }+\hat{ j }}{\sqrt{2}}$

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