For any two vectors a - and b - show that a -b - a -b -0 - a -b -

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Vector Addition

For any two v...

Question

For any two vectors $\vec{a} and \vec{b}$ , show that $(\vec{a} + \vec{b}) \cdot (\vec{a} - \vec{b}) = 0 \Leftrightarrow |\vec{a}| = |\vec{b}|$ .

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\vec{a} and \vec{b}

{|\vec{a} \times \vec{b}|}^{2} = |\begin{matrix} \vec{a} . \vec{a} & \vec{a} . \vec{b} \\ \vec{b} . \vec{a} & \vec{b} . \vec{b} \end{matrix}|

Show that $| a | b + | b | a$ is perpendicular to $| a | b - | b | a$ for any two non-zero vectors a and b.

| \to a | \to b + | \to b | \to a

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\to a

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| \to a | \to b + | \to b | \to a

| \to a | \to b - | \to b | \to a

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Show that (1+|a|^2) (1+|b|^2)=|1-a.b|^2+|a+b+a×b|^2 . For any 2 vectors a and b

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