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Assertion $(A) :$ If $(\vec{a} \times \vec{b})^2+(\vec{a} \cdot \vec{b})^2=400$ and $|\vec{a}|=4$, then $|\vec{b}|=9$.
Reason $(R) :$ If $\vec{a}$ and $\vec{b}$ are any two vectors, then $(\vec{a} \times \vec{b})^2$ is equal to $|\vec{a}|^2|\vec{b}|^2-(\vec{a} \cdot \vec{b})^2$.

• A
  Both $(A)$ and $(R)$ are true and $(R)$ is the correct explanation of $(A).$
• B
  Both $(A)$ and $(R)$ are true but $(R)$ is not the correct explanation of $(A).$
• C
  $(A)$ is true but $(R)$ is false.
• ✓
  $(A)$ is false but $(R)$ is true.