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VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA1 Mark
MCQ
Choose the correct answer from the given four options.
The position vector of the point which divides the join of points $2\vec{\text{a}}-3\vec{\text{b}}$ and $\vec{\text{a}}+\vec{\text{b}}$ in the ratio 3 : 1 is:
  • A
    $\frac{3\vec{\text{a}}-2\vec{\text{b}}}{2}$
  • B
    $\frac{7\vec{\text{a}}-8\vec{\text{b}}}{4}$
  • C
    $\frac{3\vec{\text{a}}}{4}$
  • ✓
    $\frac{5\vec{\text{a}}}{4}$
✓

Answer

Correct option: D.
$\frac{5\vec{\text{a}}}{4}$
Let the given points be $\text{A}(2\vec{\text{a}}-3\vec{\text{b}})$ and $\text{B}(\vec{\text{a}}+\vec{\text{b}})$

Let C divides AB in ratio 3 : 1

Now the position vector of a point C dividing the line segment joining the points P and Q, whose position vectors are p and q in the ratio m : n internally, is given by $\frac{\text{m}\vec{\text{q}}+\text{n}\vec{\text{p}}}{\text{m}+\text{n}}$

$\therefore$ Position vector $\text{C}=\frac{3(\vec{\text{a}}+\vec{\text{b}})+1(\vec{2\text{a}}-3\vec{\text{b}})}{3+1}$

$\Rightarrow\text{C}=\frac{5\vec{\text{a}}}{4}$

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