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VECTOR ALGEBRA — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVECTOR ALGEBRA1 Mark
Question
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:
  1. $0$
  2. $1$
  3. $\frac{3}{2}$
  4. $-\frac{5}{2}$
✓

Answer

  1. $-\frac{5}{2}$
Solution:
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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