Question

Find the value λ for which the vectors ${\displaystyle \overrightarrow{\text{a}}}$ and ${\displaystyle \overrightarrow{\text{b}}}$ are perpendicular, where ${\displaystyle \overrightarrow{\text{a}}=2\hat{\text{i}}+4\hat{\text{j}}-\hat{\text{k}}}$ and ${\displaystyle \overrightarrow{\text{b}}=3\hat{\text{i}}-2\hat{\text{j}}+\lambda \hat{\text{k}}}$

Answer 1

When ${\displaystyle \overrightarrow{\text{a}}}$ and ${\displaystyle \overrightarrow{\text{b}}}$ are ⊥^r then ${\displaystyle \overrightarrow{\text{a}}\cdot \overrightarrow{\text{b}}}$ = 0

${\displaystyle \overrightarrow{\text{a}}}$ ⊥^r  ${\displaystyle \overrightarrow{\text{b}}}$ ⇒ ${\displaystyle \overrightarrow{\text{a}}\cdot \overrightarrow{\text{b}}}$ = 0

(2)(3) + (4)(– 2) + (– 1)(λ) = 0

6 – 8 – λ = 0

– λ – 2 = 0

⇒ – λ = 2

⇒ λ = – 2