Mathematics

Problem

For

\lambda > 0

, let

\theta

be the angle between the vectors

\vec{a} = \hat{i} + \lambda \hat{j} - 3\hat{k}

and

\vec{b} = 3\hat{i} - \hat{j} + 2\hat{k}

. If the vectors

\vec{a} + \vec{b}

and

\vec{a} - \vec{b}

are mutually perpendicular, then the value of

(14 \cos \theta)^2

is equal to ![](![](https://storage.googleapis.com/diraq-contents/homework-question-parsing/marker/20260106T182719Z/a29bb5c8c9d64f6baeea92f789b45edb/30a26f2d17ca95672702bf50fb4f0242_img.jpg)) A 50 B 40 C 25 D 20

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