For any two non-zero vectors, write the value of \[\frac{\left| \vec{a} + \vec{b} \right|^2 + \left| \vec{a} - \vec{b} \right|^2}{\left| \vec{a} \right|^2 + \left| \vec{b} \right|^2} .\]

\[\text{ We have }\]\[\frac{\left| \vec{a} + \vec{b} \right|^2 + \left| \vec{a} - \vec{b} \right|^2}{\left| \vec{a} \right|^2 + \left| \vec{b} \right|^2}\]\[ = \frac{\left| \vec{a} \right|^2 + \left| \vec{b} \right|^2 + 2 \vec{a} . \vec{b} + \left| \vec{a} \right|^2 + \left| \vec{b} \right|^2 - 2 \vec{a} . \vec{b}}{\left| \vec{a} \right|^2 + \left| \vec{b} \right|^2}\]\[ = \frac{2\left( \left| \vec{a} \right|^2 + \left| \vec{b} \right|^2 \right)}{\left| \vec{a} \right|^2 + \left| \vec{b} \right|^2}\]\[ = 2\]

For Any Two Non-zero Vectors, Write the Value of ∣ ∣ → a + → B ∣ ∣ 2 + ∣ ∣ → a − → B ∣ ∣ 2 | → a | 2 + ∣ ∣ → B ∣ ∣ 2 . - Mathematics

प्रश्न

For any two non-zero vectors, write the value of $\frac{{| \vec{a} + \vec{b} |}^{2} + {| \vec{a} - \vec{b} |}^{2}}{{| \vec{a} |}^{2} + {| \vec{b} |}^{2}} .$

उत्तर

$We have$
$\frac{{| \vec{a} + \vec{b} |}^{2} + {| \vec{a} - \vec{b} |}^{2}}{{| \vec{a} |}^{2} + {| \vec{b} |}^{2}}$
$= \frac{{| \vec{a} |}^{2} + {| \vec{b} |}^{2} + 2 \vec{a} . \vec{b} + {| \vec{a} |}^{2} + {| \vec{b} |}^{2} - 2 \vec{a} . \vec{b}}{{| \vec{a} |}^{2} + {| \vec{b} |}^{2}}$
$= \frac{2 ({| \vec{a} |}^{2} + {| \vec{b} |}^{2})}{{| \vec{a} |}^{2} + {| \vec{b} |}^{2}}$
$= 2$

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Product of Two Vectors - Scalar (Or Dot) Product of Two Vectors

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अध्याय 24: Scalar Or Dot Product - very short answer [पृष्ठ ४७]

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अध्याय 24 Scalar Or Dot Product
very short answer | Q 16 | पृष्ठ ४७

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For Any Two Non-zero Vectors, Write the Value of ∣ ∣ → a + → B ∣ ∣ 2 + ∣ ∣ → a − → B ∣ ∣ 2 | → a | 2 + ∣ ∣ → B ∣ ∣ 2 . - Mathematics

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