(C) We know the Lagrange's identity for vectors: $(a \times b)^2 + (a \cdot b)^2 = |a|^2 |b|^2$. Given that $(a \times b)^2 + (a \cdot b)^2 = 144$ and

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(C) We know the Lagrange's identity for vectors: $(a \times b)^2 + (a \cdot b)^2 = |a|^2 |b|^2$. Given that $(a \times b)^2 + (a \cdot b)^2 = 144$ and $|a| = 4$. Substituting these values into the identity: $144 = (4)^2 |b|^2$ $144 = 16 |b|^2$ $|b|^2 = \frac{144}{16} = 9$ $|b| = \sqrt{9} = 3$. Thus,$|b| = 3$.