CBSE 2025 · Region 6 · Set 1 · Q19 · 1 mark

Assertion (A): If $\displaystyle |\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|^{2}+|\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}|^{2}=256$ and $\displaystyle |\overrightarrow{\mathrm{b}}|=8$, then \[|\overrightarrow{\mathrm{a}}|=2 \] Reason $\displaystyle (R): \quad \sin ^{2} \theta+\cos ^{2} \theta=1$ and \[|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|=|\overrightarrow{\mathrm{a}}||\overrightarrow{\mathrm{b}}| \sin \theta \text { and } \overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{~b}}=|\overrightarrow{\mathrm{a}}||\overrightarrow{\mathrm{b}}| \cos \theta \]

CBSE Class 12 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.