Question

If $\left|\overrightarrow{a}\right|=3,\left|\overrightarrow{b}\right|=4$, then a value of $\lambda$ for which $\overrightarrow{a}+\lambda \overrightarrow{b}$ is perpendicular to $\overrightarrow{a}-\lambda \overrightarrow{b}$ is:

• A. $\frac{9}{16}$
• B. $\frac{3}{4}$
• C. $\frac{3}{2}$
• D. $\frac{4}{3}$

Answer 1

Answer: (B)

$\frac{3}{4}$

If $\overrightarrow{a}+\lambda \overrightarrow{b}$ is perpendicular to $\overrightarrow{a}-\lambda \overrightarrow{b}$, then

$(\overrightarrow{a}+\lambda \overrightarrow{b})\cdot (\overrightarrow{a}-\lambda \overrightarrow{b})=0$

$\Rightarrow |\overrightarrow{a}{|}^2-{\lambda }^2|\overrightarrow{b}{|}^2=0$

$\Rightarrow 9-{\lambda }^2\left(16\right)=0$

$\Rightarrow \lambda =\pm \frac{3}{4}$