ધારો કે vec{a}, vec{b}, vec{c} એ અનુક્રમે 3, | vedclass

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(C) આપેલ છે કે $\vec{a} \perp (\vec{b}+\vec{c}) \implies \vec{a} \cdot (\vec{b}+\vec{c}) = 0 \implies \vec{a} \cdot \vec{b} + \vec{a} \cdot \vec{c} =

Vedclass · Accepted Answer

$5 \sqrt{2}$

Vedclass · Answer

(C) આપેલ છે કે $\vec{a} \perp (\vec{b}+\vec{c}) \implies \vec{a} \cdot (\vec{b}+\vec{c}) = 0 \implies \vec{a} \cdot \vec{b} + \vec{a} \cdot \vec{c} = 0 \quad (i)$$\vec{b} \perp (\vec{c}+\vec{a}) \implies \vec{b} \cdot (\vec{c}+\vec{a}) = 0 \implies \vec{b} \cdot \vec{c} + \vec{b} \cdot \vec{a} = 0 \quad (ii)$$\vec{c} \perp (\vec{a}+\vec{b}) \implies \vec{c} \cdot (\vec{a}+\vec{b}) = 0 \implies \vec{c} \cdot \vec{a} + \vec{c} \cdot \vec{b} = 0 \quad (iii)$$(i), (ii),$ અને $(iii)$ નો સરવાળો કરતા:$2(\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a}) = 0 \implies \vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a} = 0 \quad (iv)$હવે,$\vec{a}+\vec{b}+\vec{c}$ ની લંબાઈ નીચે મુજબ મળે:$|\vec{a}+\vec{b}+\vec{c}| = \sqrt{|\vec{a}|^2+|\vec{b}|^2+|\vec{c}|^2 + 2(\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a})}$આપેલ કિંમતો $|\vec{a}|=3, |\vec{b}|=4, |\vec{c}|=5$ અને $(iv)$ પરથી મળતું પરિણામ મૂકતા:$|\vec{a}+\vec{b}+\vec{c}| = \sqrt{3^2+4^2+5^2 + 2(0)}$$|\vec{a}+\vec{b}+\vec{c}| = \sqrt{9+16+25} = \sqrt{50} = 5\sqrt{2}$

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