Browse Questions

# Find the value of $\lambda$ for which the vectors $\overrightarrow \alpha = 3\hat i + \hat j - 2\hat k \: and \: \overrightarrow b = \hat i + \lambda\hat j - 3\hat k$ are perpendicular to each other.

Toolbox:
• If the vectors are $\perp$ ,$\overrightarrow a.\overrightarrow b=0$
• $\hat i.\hat i=1$
• $\hat j.\hat j=1$
• $\hat k.\hat k=1$
$\overrightarrow a.\overrightarrow b=(3\hat i+\hat j-2\hat k).(\hat i+\lambda \hat j-3\hat k)$
$\qquad\;=3+\lambda+6$
Since the vectors are $\perp$,then $\overrightarrow a.\overrightarrow b=0$
$\Rightarrow 3+\lambda+6=0$
$\lambda=-9$