The angle between two vectors and with magnitudes 3 and 4 respectively and = 2 3 is

Here, | | = 3 ,| | = 4 and = 2 3 As we know, 2 3 = 3 4 = 4 3 = 2 = 3

Vector Algebra — Class 12 Maths Solution

exemplar objective MCQ NCERT,Exemp,Q.No.22,Page.217

Question

The angle between two vectors $\overrightarrow {\rm{a}}$ and $\overrightarrow {\rm{b}}$ with magnitudes $\sqrt 3$ and 4 respectively and $\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} = 2\sqrt 3$ is

(a) $\frac{\pi }{6}$
(b) $\frac{\pi }{3}$ ✓ Correct
(c) $\frac{\pi }{2}$
(d) $\frac{{5\pi }}{2}$

Step-by-step Solution

Here, $|\overrightarrow {\rm{a}} | = \sqrt 3 ,|\overrightarrow {\rm{b}} | = 4$ and $\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} = 2\sqrt 3 \quad$ [given]

As we know,
$\Rightarrow$ $2\sqrt 3 = \sqrt 3 \cdot 4 \cdot \cos \theta$

$\Rightarrow$ $\cos \theta = \frac{{2\sqrt 3 }}{{4\sqrt 3 }} = \frac{1}{2}$

$\therefore \theta = \frac{\pi }{3}$

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