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# If ∣ ∣ → a + → B ∣ ∣ = 60 , ∣ ∣ → a − → B ∣ ∣ = 40 and ∣ ∣ → B ∣ ∣ = 46 , Find | → a | - CBSE (Arts) Class 12 - Mathematics

ConceptBasic Concepts of Vector Algebra

#### Question

If $\left| \vec{a} + \vec{b} \right| = 60, \left| \vec{a} - \vec{b} \right| = 40 \text{ and } \left| \vec{b} \right| = 46, \text{ find } \left| \vec{a} \right|$

#### Solution

$\text{ We know that }$
$\left| \vec{a} + \vec{b} \right|^2 + \left| \vec{a} - \vec{b} \right|^2 = 2\left( \left| \vec{a} \right|^2 + \left| \vec{b} \right|^2 \right)$
$\Rightarrow {60}^2 + {40}^2 = 2\left( \left| \vec{a} \right|^2 + {46}^2 \right) ..................(\text{ Given })$
$\Rightarrow 3600 + 1600 = 2 \left| \vec{a} \right|^2 + 4232$
$\Rightarrow 968 = 2 \left| \vec{a} \right|^2$
$\Rightarrow \left| \vec{a} \right|^2 = 484$
$\Rightarrow \left| \vec{a} \right| = 22$


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Solution If ∣ ∣ → a + → B ∣ ∣ = 60 , ∣ ∣ → a − → B ∣ ∣ = 40 and ∣ ∣ → B ∣ ∣ = 46 , Find | → a | Concept: Basic Concepts of Vector Algebra.
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