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# Solution for Find the Magnitude of Two Vectors → a and → B that Are of the Same Magnitude, Are Inclined at 60° and Whose Scalar Product is 1/2. - CBSE (Commerce) Class 12 - Mathematics

ConceptBasic Concepts of Vector Algebra

#### Question

Find the magnitude of two vectors $\vec{a} \text{ and } \vec{b}$ that are of the same magnitude, are inclined at 60° and whose scalar product is 1/2.

#### Solution

$\text{ Given that the angle between } \vec{a} \text{ and } \vec{b} {\text{ is } 30}^0 .$

$\text{ Also },$

$\left| \vec{a} \right| = \left| \vec{b} \right|; \vec{a} . \vec{b} = \frac{1}{2}$

$\text{ We know that }$

$\vec{a} . \vec{b} = \left| \vec{a} \right| \left| \vec{b} \right| \cos \theta$

$\Rightarrow \frac{1}{2} = \left| \vec{a} \right|\left| \vec{a} \right| \cos 60$

$\Rightarrow \frac{1}{2} = \left| \vec{a} \right|^2 \left( \frac{1}{2} \right)$

$\Rightarrow \left| \vec{a} \right|^2 = 1$

$\Rightarrow \left| \vec{a} \right| = 1$

$\therefore \left| \vec{a} \right| = \left| \vec{b} \right| = 1$

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Solution Find the Magnitude of Two Vectors → a and → B that Are of the Same Magnitude, Are Inclined at 60° and Whose Scalar Product is 1/2. Concept: Basic Concepts of Vector Algebra.
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