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

Question

Dr. Abubacker · Accepted Answer

(b)
Since, $\left( \overrightarrow{\mathbf{a}} + \lambda\overrightarrow{\mathbf{b}} \right) \bullet \left( \overrightarrow{\mathbf{a}} - \lambda\overrightarrow{\mathbf{b}} \right) = 0$
$\Longrightarrow ({\overrightarrow{\mathbf{a}})}^{2} - \lambda^{2}{(\overrightarrow{\mathbf{b}})}^{2} = 0$
$\Longrightarrow \ \lambda^{2}\frac{({\overrightarrow{\mathbf{a}})}^{2}}{\left( \overrightarrow{\mathbf{b}} \right)^{2}} = \left( \frac{3}{4} \right)^{2}$
$\Longrightarrow \lambda = \frac{3}{4}$

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

Explanation

Reviewed by Dr. Abubacker

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