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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.
Find the value of $\lambda$ such that the vectors $\vec{\text{a}}=2\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{a}}=\hat{\text{i}}+2\hat{\text{j}}+3\hat{\text{k}}$ are orthogonal:
  • A
    $0$
  • B
    $1$
  • C
    $\frac{3}{2}$
  • ✓
    $-\frac{5}{2}$
✓

Answer

Correct option: D.
$-\frac{5}{2}$
Given two non-zero vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ are orthogonal

$\therefore\ \vec{\text{a}}\cdot\vec{\text{b}}=0$

$\therefore\ (2\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}})\cdot(\hat{\text{i}}+2\hat{\text{j}}+\hat{3\text{k}})=0$

$\Rightarrow2+2\lambda+3=0$

$\Rightarrow\lambda=-\frac{5}{2}$

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