Vector-Algebra Question 416
Question: If $ \vec{a}=\vec{i}+2\hat{j}-3\hat{k} $ and $ \vec{b}=3\hat{i}-\hat{j}+\lambda \hat{k}, $ and $ (\vec{a}+\vec{b}) $ is perpendicular to $ \vec{a}-\vec{b} $ , then what is the value of $ \lambda $ ?
Options:
A) -2 only
B) $ \pm 2 $
C) 3 only
D) $ \pm 3 $
Correct Answer: BShow Answer
Answer:
Solution:
$ \Rightarrow (\overset{\to }{\mathop{a}},+\overset{\to }{\mathop{b}},).(\overset{\to }{\mathop{a}},-\overset{\to }{\mathop{b}},)=0 $
$ \Rightarrow {4\hat{i}+\hat{j}+(\lambda -3)\hat{k}}{-2\hat{i}+3\hat{j}-(3-\lambda )\hat{k}}=0 $
$ \Rightarrow -8+3+(3^{2}-{{\lambda }^{2}})=0 $
$ \Rightarrow -4-{{\lambda }^{2}}=0 $
$ \Rightarrow \lambda =\pm ,2 $
BETA
