Find the angle between two vectors a and b with magnitudes 3 and 2 respectively, having a b = 6 .

If be the angle between a and b , then = | a|| b| = 3 (2) = ( 3 )(2) = 2 = 4 . Hence, = 4 .

Vector Algebra — Class 12 Maths Solution

ncert exercise SA NCERT,Page 447,Ex.10.3,Q.No 1

Question

Find the angle between two vectors $\vec a$ and $\vec b$ with magnitudes $\sqrt 3$ and $2$ respectively, having $\vec a \cdot \vec b = \sqrt 6$.

Step-by-step Solution

If $\theta$ be the angle between $\vec a$ and $\vec b$, then
$\cos \theta = \cfrac{{\vec a.\vec b}}{{|\vec a||\vec b|}} = \cfrac{{\sqrt 6 }}{{\sqrt 3 (2)}} = \cfrac{{(\sqrt 3 ).(\sqrt 2 )}}{{(\sqrt 3 )(2)}} = \cfrac{1}{{\sqrt 2 }} = \cos \cfrac{\pi }{4}$.
Hence, $\theta = \cfrac{\pi }{4}$.

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Vector Algebra. Curated by Sachin Sharma. Free for all students.